/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Egor Kulikov
 */

// Actual solution is at the bottom





#include <bits/stdc++.h>

using namespace std;

#define all(v) (v).begin(), (v).end()
#define val const auto&

using ll = long long;
using ull = unsigned long long;
using li = __int128;
using uli = unsigned __int128;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;

void doReplace() {
}

template <typename T, typename U, typename...Vs>
void doReplace(T& t, const U& u, Vs&& ...vs) {
    t = u;
    doReplace(vs...);
}

template <typename T, typename...Us>
T minim(T& was, const T& cand, Us&& ...us) {
    if (was > cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}

template <typename T, typename...Us>
T maxim(T& was, const T& cand, Us&& ...us) {
    if (was < cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}


template <typename D>
D dPower(D base, ll exponent) {
    if (exponent < 0) {
        return dPower(1 / base, -exponent);
    }
    if (exponent == 0) {
        return 1;
    }
    if ((exponent & 1) == 1) {
        return dPower(base, exponent - 1) * base;
    } else {
        D res = dPower(base, exponent >> 1);
        return res * res;
    }
}


class NumberIterator : iterator<forward_iterator_tag, int> {
public:
    int v;

    NumberIterator(int v) : v(v) {}

    operator int&() { return v; }

    int operator*() { return v; }
};

class range : pii {
public:
    range(int begin, int end) : pii(begin, max(begin, end)) {}

    range(int n) : pii(0, max(0, n)) {}

    NumberIterator begin() {
        return first;
    }

    NumberIterator end() {
        return second;
    }
};


template <typename T>
class NeedFill {
    struct Fallback {
        int begin;
    }; // add member name "find"
    struct Derived : T, Fallback {
    };

    template <typename U, U>
    struct Check;

    typedef char Yes[1];  // typedef for an array of size one.
    typedef char No[2];  // typedef for an array of size two.

    template <typename U>
    static No& func(Check<int Fallback::*, &U::begin>*);

    template <typename U>
    static Yes& func(...);

public:
    typedef NeedFill type;
    enum {
        value = sizeof(func<Derived>(0)) == sizeof(Yes)
    };
};

template <>
class NeedFill<int> {
public:
    const static bool value = false;
};

template <>
class NeedFill<unsigned> {
public:
    const static bool value = false;
};

template <>
class NeedFill<ull> {
public:
    const static bool value = false;
};

template <>
class NeedFill<uli> {
public:
    const static bool value = false;
};

template <>
class NeedFill<bool> {
public:
    const static bool value = true;
};

template <>
class NeedFill<ll> {
public:
    const static bool value = false;
};

template <>
class NeedFill<double> {
public:
    const static bool value = false;
};

template <>
class NeedFill<ld> {
public:
    const static bool value = false;
};

template <>
class NeedFill<char> {
public:
    const static bool value = false;
};

template <typename T>
class arr {
    T* b;
    int n;

    void allocate(int sz) {
#ifdef LOCAL
        if (sz < 0) {
            throw "bad alloc";
        }
#endif
        n = sz;
        if (sz > 0) {
            b = (T*) (::operator new(sz * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr(int n = 0) {
        allocate(n);
        if (NeedFill<T>::value) {
            for (int i : range(n)) {
                ::new((void*) (b + i)) T;
            }
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(int n, const T& init) {
        allocate(n);
        for (int i : range(n)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(T* b, int n) : arr(b, b + n) {}

    arr(T* b, T* e) : b(b), n(e - b) {}

    arr(initializer_list<T> l) : arr(l.size()) {
        if (n > 0) {
            memcpy(b, l.begin(), n * sizeof(T));
        }
    }

    int size() const {
        return n;
    }

    T* begin() {
        return b;
    }

    const T* begin() const {
        return b;
    }

    T* end() {
        return b + n;
    }

    const T* end() const {
        return b + n;
    }

    arr<T> clone() const {
        arr<T> res(n);
        copy(b, b + n, res.begin());
        return res;
    }

    T& operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    const T& operator[](int at) const {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    bool operator==(const arr& other) const {
        if (n != other.n) {
            return false;
        }
        for (int i : range(n)) {
            if (b[i] != other.b[i]) {
                return false;
            }
        }
        return true;
    }

    vector<T> view() {
        return vector<T>(b, b + n);
    }

    arr<T> subArray(int from, int to) const {
        return arr<T>(b + from, b + to);
    }
};

typedef arr<int> arri;

void decreaseByOne() {}

template <typename T, class...Vs>
void decreaseByOne(arr<T>& array, Vs& ...vs) {
    int n = array.size();
    for (int i : range(n)) {
        array[i]--;
    }
    decreaseByOne(vs...);
}


template <typename T>
class arr2d {
    T* b;
    int d1;
    int d2;
    int sz;

    void allocate(int n) {
#ifdef LOCAL
        if (n < 0) {
            throw "bad alloc";
        }
#endif
        if (n > 0) {
            b = (T*) (::operator new(n * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr2d(int d1 = 0, int d2 = 0) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        if (NeedFill<T>::value) {
            for (int i : range(sz)) {
                ::new((void*) (b + i)) T;
            }
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(int d1, int d2, const T& init) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        for (int i : range(sz)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(T* b, int d1, int d2) : b(b), d1(d1), d2(d2), sz(d1 * d2) {}

    int size() const {
        return sz;
    }

    int dim1() const {
        return d1;
    }

    int dim2() const {
        return d2;
    }

    T* begin() {
        return b;
    }

    T* end() {
        return b + sz;
    }

    T& operator()(int i1, int i2) {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    const T& operator()(int i1, int i2) const {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    T& operator[](const pii& p) {
        return operator()(p.first, p.second);
    }

    const T& operator[](const pii& p) const {
        return operator()(p.first, p.second);
    }

    arr<T> operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= d1) {
            throw "Out of bounds";
        }
#endif
        return arr<T>(b + at * d2, d2);
    }

    vector<vector<T>> view() {
        vector<vector<T>> res(min(d1, 50));
        for (int i : range(res.size())) {
            res[i] = (*this)[i].view();
        }
        return res;
    }

};


inline bool isWhitespace(int c) {
    return isspace(c) || c == EOF;
}

class Input {
private:
    bool exhausted = false;
    int bufSize = 4096;
    char* buf = new char[bufSize];
    int bufRead = 0;
    int bufAt = 0;

public:
    inline int get() {
        if (exhausted) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            return EOF;
        }
        return buf[bufAt++];
    }

    inline int peek() {
        if (exhausted) {
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            getchar();
            return EOF;
        }
        return buf[bufAt];
    }

private:
    template <typename T>
    inline T readInteger() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        } else if (c == '+') {
            c = get();
        }
        T res = 0;
        do {
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c));
        return res * sgn;
    }

    void initArrays(int) {}

    template <typename T, class...Vs>
    void initArrays(int n, arr<T>& array, Vs& ...vs) {
        array = arr<T>(n);
        initArrays(n, vs...);
    }

    template <typename T, class...Vs>
    void initArrays(int n, vector<T>&, Vs& ...vs) {
        initArrays(n, vs...);
    }

    void readImpl(int) {}

    template <typename T, class...Vs>
    void readImpl(int i, arr<T>& arr, Vs& ...vs) {
        arr[i] = readType<T>();
        readImpl(i, vs...);
    }

    template <typename T, class...Vs>
    void readImpl(int i, vector<T>& arr, Vs& ...vs) {
        arr.push_back(readType<T>());
        readImpl(i, vs...);
    }

public:
    inline int skipWhitespace() {
        int c;
        while (isWhitespace(c = get()) && c != EOF);
        return c;
    }

    inline int peekNext() {
        while (isWhitespace(peek()) && peek() != EOF) {
            get();
        }
        return peek();
    }

    inline int readInt() {
        return readInteger<int>();
    }

    inline ll readLong() {
        return readInteger<ll>();
    }

    inline unsigned readUnsigned() {
        return readInteger<unsigned>();
    }

    string readString() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        do {
            res.push_back(c);
        } while (!isWhitespace(c = get()));
        return res;
    }

    arri readIntArray(int size) {
        return readArray<int>(size);
    }

    arr<ll> readLongArray(int size) {
        return readArray<ll>(size);
    }

    arr<double> readDoubleArray(int size) {
        return readArray<double>(size);
    }

    arr<string> readStringArray(int size) {
        return readArray<string>(size);
    }

    arr<char> readCharArray(int size) {
        return readArray<char>(size);
    }

    template <typename T>
    T readType() {
        throw "Operation not supported";
    }

    template <typename U, typename V>
    pair<U, V> readType() {
        U first = readType<U>();
        V second = readType<V>();
        return make_pair(first, second);
    }

    template <typename T>
    arr<T> readArray(int n) {
        arr<T> res(n, T());
        for (int i : range(n)) {
            res[i] = readType<T>();
        }
        return res;
    }


    template <class...Vs>
    void readArrays(int n, Vs& ...vs) {
        initArrays(n, vs...);
        for (int i : range(n)) {
            readImpl(i, vs...);
        }
    }

    template <typename U, typename V>
    arr<pair<U, V>> readArray(int n) {
        arr<pair<U, V>> res(n);
        for (int i : range(n)) {
            res[i] = readType<U, V>();
        }
        return res;
    }

    template <typename T>
    arr2d<T> readTable(int rows, int cols) {
        arr2d<T> result(rows, cols);
        for (int i : range(rows)) {
            for (int j : range(cols)) {
                result(i, j) = readType<T>();
            }
        }
        return result;
    }

    arr2d<int> readIntTable(int rows, int cols) {
        return readTable<int>(rows, cols);
    }

    arr2d<char> readCharTable(int rows, int cols) {
        return readTable<char>(rows, cols);
    }

    string readLine() {
        int c = get();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        while (c != '\n' && c != '\r' && c != EOF) {
            res.push_back(c);
            c = get();
        }
        if (c == '\r' && peek() == '\n') {
            get();
        }
        return res;
    }

    inline double readDouble() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        double res = 0;
        do {
            if (tolower(c) == 'e') {
                return sgn * res * dPower(double(10), readInt());
            }
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c) && c != '.');
        if (c == '.') {
            double add = 0;
            int length = 0;
            c = get();
            do {
                if (tolower(c) == 'e') {
                    return sgn * (res + add * dPower(double(10), -length)) * dPower(double(10), readInt());
                }
                if (!isdigit(c)) {
#ifdef LOCAL
                    throw "Number format error";
#endif
                    res += add * dPower(10, -length);
                    return res * sgn;
                }
                add *= 10;
                add += c - '0';
                length++;
                c = get();
            } while (!isWhitespace(c));
            res += add * dPower(double(10), -length);
        }
        return res * sgn;
    }

    inline char readChar() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return 0;
        }
        return c;
    }

    inline bool isExhausted() { return exhausted; }

    inline void setBufSize(int newBufSize) {
        if (newBufSize > bufSize) {
            char* newBuf = new char[newBufSize];
            memcpy(newBuf, buf, bufSize);
            buf = newBuf;
        }
        bufSize = newBufSize;
    }
};

template <>
inline double Input::readType() {
    return readDouble();
}

template <>
inline int Input::readType() {
    return readInt();
}

template <>
inline ll Input::readType() {
    return readLong();
}

template <>
inline unsigned Input::readType() {
    return readUnsigned();
}

template <>
inline char Input::readType() {
    return readChar();
}

template <>
inline string Input::readType() {
    return readString();
}

Input in;


class Output {
private:
    ostream* out;

    template <typename T>
    inline void printSingle(const T& value) {
        *out << value;
    }

    template <typename T>
    void printSingle(const vector<T>& array) {
        size_t n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr<T>& array) {
        int n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr2d<T>& array) {
        size_t n = array.dim1();
        size_t m = array.dim2();
        for (int i : range(n)) {
            for (int j : range(m)) {
                *out << array(i, j);
                if (j + 1 != m) {
                    *out << ' ';
                }
            }
            if (i + 1 != n) {
                *out << '\n';
            }
        }
    }

    template <typename T, typename U>
    inline void printSingle(const pair<T, U>& value) {
        *out << value.first << ' ' << value.second;
    }

public:
    bool autoflush;

    Output(ostream& out, bool autoflush) : out(&out), autoflush(autoflush) {
        setPrecision(20);
    }

    void setOut(ostream& nOut) {
        out = &nOut;
        setPrecision(20);
    }

    inline void print() {}

    template <typename T, typename...Targs>
    inline void print(const T& first, const Targs... args) {
        printSingle(first);
        if (sizeof...(args) != 0) {
            *out << ' ';
            print(args...);
        }
        if (autoflush) {
            flush();
        }
    }

    template <typename...Targs>
    inline void printLine(const Targs... args) {
        print(args...);
        *out << '\n';
        if (autoflush) {
            flush();
        }
    }

    inline void flush() {
        out->flush();
    }

    inline void setPrecision(int digs) {
        *out << fixed << setprecision(digs);
    }
};

Output out(cout, false);
Output err(cerr, true);

#ifdef LOCAL
#define debug(x) err.printLine(#x, '=', x);
#else
#define debug(x)
#endif


const int MOD7 = 1000000007;
const int MOD9 = 1000000009;
const int MODF = 998244353;

int mod = MOD7;

ll gcd(ll a, ll b, ll& x, ll& y) {
    if (a == 0) {
        x = 0;
        y = 1;
        return b;
    }
    int d = gcd(b % a, a, y, x);
    x -= (b / a) * y;
    return d;
}

class modint {
public:
    int n;

    modint() : n(0) {}

    modint(ll n, bool special = false) {
        if (special) {
            this->n = -1;
            return;
        }
        if (n >= 0 && n < mod) {
            this->n = n;
            return;
        }
        n %= mod;
        if (n < 0) {
            n += mod;
        }
        this->n = n;
    }

    modint& operator+=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n += other.n;
        if (n >= mod) {
            n -= mod;
        }
        return *this;
    }

    modint& operator-=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n -= other.n;
        if (n < 0) {
            n += mod;
        }
        return *this;
    }

    modint& operator*=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n = ll(n) * other.n % mod;
        return *this;
    }

    modint& operator/=(const modint& other) {
#ifdef LOCAL
        if (other.n == 0) {
            throw "Division by zero";
        }
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        return *this *= other.inverse();
    }

    modint operator-() {
#ifdef LOCAL
        if (n == -1) {
            throw "Illegal state";
        }
#endif
        if (n == 0) {
            return 0;
        }
        return modint(mod - n);
    }

    modint inverse() const {
#ifdef LOCAL
        if (n == -1) {
            throw "Illegal state";
        }
#endif
        ll x, y;
        ll g = gcd(ll(n), ll(mod), x, y);
#ifdef LOCAL
        if (g != 1) {
            throw "not inversable";
        }
#endif
        return x;
    }

    int log(modint alpha);
};

modint nullModint(-1, true);

modint operator+(const modint& a, const modint& b) {
    return modint(a) += b;
}

modint operator-(const modint& a, const modint& b) {
    return modint(a) -= b;
}

modint operator*(const modint& a, const modint& b) {
    return modint(a) *= b;
}

modint operator/(const modint& a, const modint& b) {
    return modint(a) /= b;
}

ostream& operator<<(ostream& out, const modint& v) {
    return out << v.n;
}

bool operator==(const modint& a, const modint& b) {
    return a.n == b.n;
}

bool operator!=(const modint& a, const modint& b) {
    return a.n != b.n;
}

namespace std {
    template <>
    struct hash<modint> {
        size_t operator()(const modint& n) const {
            return n.n;
        }
    };
}

int modint::log(modint alpha) {
#ifdef LOCAL
    if (n == -1 || alpha.n == -1) {
        throw "Illegal state";
    }
#endif
    unordered_map<modint, int> base;
    int exp = 0;
    modint pow = 1;
    modint inv = *this;
    modint alInv = alpha.inverse();
    while (exp * exp < mod) {
        if (inv == 1) {
            return exp;
        }
        base[inv] = exp++;
        pow *= alpha;
        inv *= alInv;
    }
    modint step = pow;
    for (int i = 1;; i++) {
        if (base.count(pow)) {
            return exp * i + base[pow];
        }
        pow *= step;
    }
}


class ETsinshanIDaniel {
public:
    void solve() {
        int n = in.readInt();
        int m = in.readInt();
        arri p, k, b, w;
        in.readArrays(m, p, k, b, w);

        modint seed = 0;
        int base = 0;
        arri t(n);
        arri a(n);
        auto rnd = [&]() -> int {
            int res = seed.n;
            seed = seed * base + 233;
            return res;
        };
        int last = 0;
        for (int i : range(m)) {
            seed = b[i];
            base = w[i];
            for (int j : range(last, p[i])) {
                t[j] = rnd() & 1;
                a[j] = rnd() % k[i] + 1;
            }
            last = p[i];
        }
        ll total1 = 0;
        ll total2 = 0;
        for (int i : range(n)) {
            if (t[i] == 0) {
                total1 += a[i];
            } else {
                total2 += a[i];
            }
        }
        if (total1 > total2) {
            for (int i : range(n)) {
                t[i] = 1 - t[i];
            }
        }
        arri ans(n, 0);
        if (t[0] == 1) {
            ans[0] = 1;
        }
        int at = 0;
        for (int i : range(n)) {
            if (i == at) {
                at++;
                if (at == n) {
                    at = 0;
                }
            }
            if (t[i] == 1) {
                continue;
            }
            ans[i] = a[i];
            int rem = a[i];
            while (rem > 0) {
                while (t[at] == 0 || ans[at] == a[at]) {
                    at++;
                    if (at == n) {
                        at = 0;
                    }
                }
                int cur = min(rem, a[at] - ans[at]);
                ans[at] += cur;
                rem -= cur;
            }
        }
        modint answer = 1;
        for (int i : range(n)) {
            answer *= (ans[i] ^ (ll(i + 1) * (i + 1))) + 1;
        }
        out.printLine(answer);
    }
};


int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
#ifdef LOCAL_RELEASE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    auto time = clock();
#endif
    ETsinshanIDaniel solver;


    solver.solve();
    fflush(stdout);
#ifdef LOCAL_RELEASE
    cerr << setprecision(3) << double(clock() - time) / CLOCKS_PER_SEC << endl;
#endif
    return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Qingshan and Daniel are going to play a card game. But it will be so boring if only two persons play this. So they will make n robots in total to play this game automatically. Robots made by Qingshan belong to the team 1, and robots made by Daniel belong to the team 2. Robot i belongs to team t_i. Before the game starts, a_i cards are given for robot i.

The rules for this card game are simple: 

  * Before the start, the robots are arranged in a circle in the order or their indices. The robots will discard cards in some order, in each step one robot discards a single card. When the game starts, robot 1 will discard one of its cards. After that, robots will follow the following rules: 
  * If robot i discards the card last, the nearest robot whose team is opposite from i's will discard the card next. In another word j will discard a card right after i, if and only if among all j that satisfy t_i≠ t_j, dist(i,j) (definition is below) is minimum. 
  * The robot who has no cards should quit the game immediately. This robot won't be considered in the next steps. 
  * When no robot can discard the card next, the game ends. 



We define the distance from robot x to robot y as dist(x,y)=(y-x+n)mod n. It is similar to the oriented distance on the circle.

For example, when n=5, the distance from 1 to 3 is dist(1,3)=(3-1+5)mod 5=2, the distance from 3 to 1 is dist(3,1)=(1-3+5)mod 5 =3.

Later, Qingshan finds out that it will take so much time to see how robots play. She wants to know the result as quickly as possible. You, as Qingshan's fan, are asked to calculate an array [ans_1,ans_2,…,ans_n] — ans_i is equal to the number of cards, that i-th robot will discard during the game. You need to hurry!

To avoid the large size of the input, the team and the number of cards of each robot will be generated in your code with some auxiliary arrays.

Input

The first line contains one integer n (1 ≤ n ≤ 5⋅ 10^6) — the number of robots playing this game.

The second line contains one integer m (1 ≤ m ≤ min(n,200 000)).

Each of the next m line contains four integers p_i, k_i, b_i, w_i (1 ≤ p_i ≤ n, 1 ≤ k_i ≤ 10^9+7, 0 ≤ b_i ,w_i< k_i). It's guaranteed that p_m=n and p_{j-1}<p_{j} (2 ≤ j ≤ m).

Arrays a_j and t_j should be generated by the following pseudo code:
    
    
      
    seed = 0  
    base = 0  
      
    function rnd():  
    	ret = seed  
    	seed = (seed * base + 233) mod 1000000007  
    	return ret  
      
    p[0] = 0  
    for i = 1 to m:  
    	seed = b[i]  
    	base = w[i]  
    	for j = p[i - 1] + 1 to p[i]:  
    		t[j] = (rnd() mod 2) + 1  
    		a[j] = (rnd() mod k[i]) + 1  
    

Output

Print a single integer \left( ∏_{i=1}^{n} ((ans_i ⊕ i^2)+1)\right) mod 10^9+7, where ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR).

Examples

Input


3
3
1 5 2 3
2 7 1 2
3 2 1 1


Output


100


Input


5000000
2
1919810 998244353 114514 19260817
5000000 233333333 623532 7175


Output


800210675


Input


1
1
1 1 0 0


Output


1

Note

In the first test case a=[5,5,1] and t=[1,2,2].

The robot 1 discards the card first.

Then robot 2 discards the card next. Robot 3 doesn't discard the card next because dist(1,2)<dist(1,3).

Then robot 1 discards the card next. Robot 3 doesn't discard the card next because t_2=t_3.

If we write down the index of the robot who discards a card in time order, it will be the sequence [1,2,1,2,1,2,1,2]. So robots 1, 2 and 3 discard 5, 5 and 0 cards, respectively. And the answer is (((5 ⊕ 1^2)+1)×((5 ⊕ 2^2)+1)×((0 ⊕ 3^2)+1)) mod 10^9+7=(5× 2 × 10)mod 10^9+7=100.

### Response

```cpp
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Egor Kulikov
 */

// Actual solution is at the bottom





#include <bits/stdc++.h>

using namespace std;

#define all(v) (v).begin(), (v).end()
#define val const auto&

using ll = long long;
using ull = unsigned long long;
using li = __int128;
using uli = unsigned __int128;
using ld = long double;
using pii = pair<int, int>;
using vi = vector<int>;

void doReplace() {
}

template <typename T, typename U, typename...Vs>
void doReplace(T& t, const U& u, Vs&& ...vs) {
    t = u;
    doReplace(vs...);
}

template <typename T, typename...Us>
T minim(T& was, const T& cand, Us&& ...us) {
    if (was > cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}

template <typename T, typename...Us>
T maxim(T& was, const T& cand, Us&& ...us) {
    if (was < cand) {
        was = cand;
        doReplace(us...);
    }
    return was;
}


template <typename D>
D dPower(D base, ll exponent) {
    if (exponent < 0) {
        return dPower(1 / base, -exponent);
    }
    if (exponent == 0) {
        return 1;
    }
    if ((exponent & 1) == 1) {
        return dPower(base, exponent - 1) * base;
    } else {
        D res = dPower(base, exponent >> 1);
        return res * res;
    }
}


class NumberIterator : iterator<forward_iterator_tag, int> {
public:
    int v;

    NumberIterator(int v) : v(v) {}

    operator int&() { return v; }

    int operator*() { return v; }
};

class range : pii {
public:
    range(int begin, int end) : pii(begin, max(begin, end)) {}

    range(int n) : pii(0, max(0, n)) {}

    NumberIterator begin() {
        return first;
    }

    NumberIterator end() {
        return second;
    }
};


template <typename T>
class NeedFill {
    struct Fallback {
        int begin;
    }; // add member name "find"
    struct Derived : T, Fallback {
    };

    template <typename U, U>
    struct Check;

    typedef char Yes[1];  // typedef for an array of size one.
    typedef char No[2];  // typedef for an array of size two.

    template <typename U>
    static No& func(Check<int Fallback::*, &U::begin>*);

    template <typename U>
    static Yes& func(...);

public:
    typedef NeedFill type;
    enum {
        value = sizeof(func<Derived>(0)) == sizeof(Yes)
    };
};

template <>
class NeedFill<int> {
public:
    const static bool value = false;
};

template <>
class NeedFill<unsigned> {
public:
    const static bool value = false;
};

template <>
class NeedFill<ull> {
public:
    const static bool value = false;
};

template <>
class NeedFill<uli> {
public:
    const static bool value = false;
};

template <>
class NeedFill<bool> {
public:
    const static bool value = true;
};

template <>
class NeedFill<ll> {
public:
    const static bool value = false;
};

template <>
class NeedFill<double> {
public:
    const static bool value = false;
};

template <>
class NeedFill<ld> {
public:
    const static bool value = false;
};

template <>
class NeedFill<char> {
public:
    const static bool value = false;
};

template <typename T>
class arr {
    T* b;
    int n;

    void allocate(int sz) {
#ifdef LOCAL
        if (sz < 0) {
            throw "bad alloc";
        }
#endif
        n = sz;
        if (sz > 0) {
            b = (T*) (::operator new(sz * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr(int n = 0) {
        allocate(n);
        if (NeedFill<T>::value) {
            for (int i : range(n)) {
                ::new((void*) (b + i)) T;
            }
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(int n, const T& init) {
        allocate(n);
        for (int i : range(n)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr(T* b, int n) : arr(b, b + n) {}

    arr(T* b, T* e) : b(b), n(e - b) {}

    arr(initializer_list<T> l) : arr(l.size()) {
        if (n > 0) {
            memcpy(b, l.begin(), n * sizeof(T));
        }
    }

    int size() const {
        return n;
    }

    T* begin() {
        return b;
    }

    const T* begin() const {
        return b;
    }

    T* end() {
        return b + n;
    }

    const T* end() const {
        return b + n;
    }

    arr<T> clone() const {
        arr<T> res(n);
        copy(b, b + n, res.begin());
        return res;
    }

    T& operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    const T& operator[](int at) const {
#ifdef LOCAL
        if (at < 0 || at >= n) {
            throw "Out of bounds";
        }
#endif
        return b[at];
    }

    bool operator==(const arr& other) const {
        if (n != other.n) {
            return false;
        }
        for (int i : range(n)) {
            if (b[i] != other.b[i]) {
                return false;
            }
        }
        return true;
    }

    vector<T> view() {
        return vector<T>(b, b + n);
    }

    arr<T> subArray(int from, int to) const {
        return arr<T>(b + from, b + to);
    }
};

typedef arr<int> arri;

void decreaseByOne() {}

template <typename T, class...Vs>
void decreaseByOne(arr<T>& array, Vs& ...vs) {
    int n = array.size();
    for (int i : range(n)) {
        array[i]--;
    }
    decreaseByOne(vs...);
}


template <typename T>
class arr2d {
    T* b;
    int d1;
    int d2;
    int sz;

    void allocate(int n) {
#ifdef LOCAL
        if (n < 0) {
            throw "bad alloc";
        }
#endif
        if (n > 0) {
            b = (T*) (::operator new(n * sizeof(T)));
        } else {
            b = nullptr;
        }
    }

public:
    arr2d(int d1 = 0, int d2 = 0) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        if (NeedFill<T>::value) {
            for (int i : range(sz)) {
                ::new((void*) (b + i)) T;
            }
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(int d1, int d2, const T& init) : d1(d1), d2(d2), sz(d1 * d2) {
#ifdef LOCAL
        if (d1 < 0 || d2 < 0) {
            throw "bad alloc";
        }
#endif
        allocate(sz);
        for (int i : range(sz)) {
            ::new((void*) (b + i)) T(init);
        }
#ifdef LOCAL
        view();
#endif
    }

    arr2d(T* b, int d1, int d2) : b(b), d1(d1), d2(d2), sz(d1 * d2) {}

    int size() const {
        return sz;
    }

    int dim1() const {
        return d1;
    }

    int dim2() const {
        return d2;
    }

    T* begin() {
        return b;
    }

    T* end() {
        return b + sz;
    }

    T& operator()(int i1, int i2) {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    const T& operator()(int i1, int i2) const {
#ifdef LOCAL
        if (i1 < 0 || i1 >= d1 || i2 < 0 || i2 >= d2) {
            throw "Out of bounds";
        }
#endif
        return b[i1 * d2 + i2];
    }

    T& operator[](const pii& p) {
        return operator()(p.first, p.second);
    }

    const T& operator[](const pii& p) const {
        return operator()(p.first, p.second);
    }

    arr<T> operator[](int at) {
#ifdef LOCAL
        if (at < 0 || at >= d1) {
            throw "Out of bounds";
        }
#endif
        return arr<T>(b + at * d2, d2);
    }

    vector<vector<T>> view() {
        vector<vector<T>> res(min(d1, 50));
        for (int i : range(res.size())) {
            res[i] = (*this)[i].view();
        }
        return res;
    }

};


inline bool isWhitespace(int c) {
    return isspace(c) || c == EOF;
}

class Input {
private:
    bool exhausted = false;
    int bufSize = 4096;
    char* buf = new char[bufSize];
    int bufRead = 0;
    int bufAt = 0;

public:
    inline int get() {
        if (exhausted) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            return EOF;
        }
        return buf[bufAt++];
    }

    inline int peek() {
        if (exhausted) {
            return EOF;
        }
        if (bufRead == bufAt) {
            bufRead = fread(buf, sizeof(char), bufSize, stdin);
            bufAt = 0;
        }
        if (bufRead == bufAt) {
            exhausted = true;
            getchar();
            return EOF;
        }
        return buf[bufAt];
    }

private:
    template <typename T>
    inline T readInteger() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        } else if (c == '+') {
            c = get();
        }
        T res = 0;
        do {
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c));
        return res * sgn;
    }

    void initArrays(int) {}

    template <typename T, class...Vs>
    void initArrays(int n, arr<T>& array, Vs& ...vs) {
        array = arr<T>(n);
        initArrays(n, vs...);
    }

    template <typename T, class...Vs>
    void initArrays(int n, vector<T>&, Vs& ...vs) {
        initArrays(n, vs...);
    }

    void readImpl(int) {}

    template <typename T, class...Vs>
    void readImpl(int i, arr<T>& arr, Vs& ...vs) {
        arr[i] = readType<T>();
        readImpl(i, vs...);
    }

    template <typename T, class...Vs>
    void readImpl(int i, vector<T>& arr, Vs& ...vs) {
        arr.push_back(readType<T>());
        readImpl(i, vs...);
    }

public:
    inline int skipWhitespace() {
        int c;
        while (isWhitespace(c = get()) && c != EOF);
        return c;
    }

    inline int peekNext() {
        while (isWhitespace(peek()) && peek() != EOF) {
            get();
        }
        return peek();
    }

    inline int readInt() {
        return readInteger<int>();
    }

    inline ll readLong() {
        return readInteger<ll>();
    }

    inline unsigned readUnsigned() {
        return readInteger<unsigned>();
    }

    string readString() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        do {
            res.push_back(c);
        } while (!isWhitespace(c = get()));
        return res;
    }

    arri readIntArray(int size) {
        return readArray<int>(size);
    }

    arr<ll> readLongArray(int size) {
        return readArray<ll>(size);
    }

    arr<double> readDoubleArray(int size) {
        return readArray<double>(size);
    }

    arr<string> readStringArray(int size) {
        return readArray<string>(size);
    }

    arr<char> readCharArray(int size) {
        return readArray<char>(size);
    }

    template <typename T>
    T readType() {
        throw "Operation not supported";
    }

    template <typename U, typename V>
    pair<U, V> readType() {
        U first = readType<U>();
        V second = readType<V>();
        return make_pair(first, second);
    }

    template <typename T>
    arr<T> readArray(int n) {
        arr<T> res(n, T());
        for (int i : range(n)) {
            res[i] = readType<T>();
        }
        return res;
    }


    template <class...Vs>
    void readArrays(int n, Vs& ...vs) {
        initArrays(n, vs...);
        for (int i : range(n)) {
            readImpl(i, vs...);
        }
    }

    template <typename U, typename V>
    arr<pair<U, V>> readArray(int n) {
        arr<pair<U, V>> res(n);
        for (int i : range(n)) {
            res[i] = readType<U, V>();
        }
        return res;
    }

    template <typename T>
    arr2d<T> readTable(int rows, int cols) {
        arr2d<T> result(rows, cols);
        for (int i : range(rows)) {
            for (int j : range(cols)) {
                result(i, j) = readType<T>();
            }
        }
        return result;
    }

    arr2d<int> readIntTable(int rows, int cols) {
        return readTable<int>(rows, cols);
    }

    arr2d<char> readCharTable(int rows, int cols) {
        return readTable<char>(rows, cols);
    }

    string readLine() {
        int c = get();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return "";
        }
        string res;
        while (c != '\n' && c != '\r' && c != EOF) {
            res.push_back(c);
            c = get();
        }
        if (c == '\r' && peek() == '\n') {
            get();
        }
        return res;
    }

    inline double readDouble() {
        int c = skipWhitespace();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = get();
        }
        double res = 0;
        do {
            if (tolower(c) == 'e') {
                return sgn * res * dPower(double(10), readInt());
            }
            if (!isdigit(c)) {
#ifdef LOCAL
                throw "Number format error";
#endif
                return sgn * res;
            }
            res *= 10;
            res += c - '0';
            c = get();
        } while (!isWhitespace(c) && c != '.');
        if (c == '.') {
            double add = 0;
            int length = 0;
            c = get();
            do {
                if (tolower(c) == 'e') {
                    return sgn * (res + add * dPower(double(10), -length)) * dPower(double(10), readInt());
                }
                if (!isdigit(c)) {
#ifdef LOCAL
                    throw "Number format error";
#endif
                    res += add * dPower(10, -length);
                    return res * sgn;
                }
                add *= 10;
                add += c - '0';
                length++;
                c = get();
            } while (!isWhitespace(c));
            res += add * dPower(double(10), -length);
        }
        return res * sgn;
    }

    inline char readChar() {
        int c = skipWhitespace();
        if (c == EOF) {
#ifdef LOCAL
            throw "Input exhausted";
#endif
            return 0;
        }
        return c;
    }

    inline bool isExhausted() { return exhausted; }

    inline void setBufSize(int newBufSize) {
        if (newBufSize > bufSize) {
            char* newBuf = new char[newBufSize];
            memcpy(newBuf, buf, bufSize);
            buf = newBuf;
        }
        bufSize = newBufSize;
    }
};

template <>
inline double Input::readType() {
    return readDouble();
}

template <>
inline int Input::readType() {
    return readInt();
}

template <>
inline ll Input::readType() {
    return readLong();
}

template <>
inline unsigned Input::readType() {
    return readUnsigned();
}

template <>
inline char Input::readType() {
    return readChar();
}

template <>
inline string Input::readType() {
    return readString();
}

Input in;


class Output {
private:
    ostream* out;

    template <typename T>
    inline void printSingle(const T& value) {
        *out << value;
    }

    template <typename T>
    void printSingle(const vector<T>& array) {
        size_t n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr<T>& array) {
        int n = array.size();
        for (int i : range(n)) {
            *out << array[i];
            if (i + 1 != n) {
                *out << ' ';
            }
        }
    }

    template <typename T>
    void printSingle(const arr2d<T>& array) {
        size_t n = array.dim1();
        size_t m = array.dim2();
        for (int i : range(n)) {
            for (int j : range(m)) {
                *out << array(i, j);
                if (j + 1 != m) {
                    *out << ' ';
                }
            }
            if (i + 1 != n) {
                *out << '\n';
            }
        }
    }

    template <typename T, typename U>
    inline void printSingle(const pair<T, U>& value) {
        *out << value.first << ' ' << value.second;
    }

public:
    bool autoflush;

    Output(ostream& out, bool autoflush) : out(&out), autoflush(autoflush) {
        setPrecision(20);
    }

    void setOut(ostream& nOut) {
        out = &nOut;
        setPrecision(20);
    }

    inline void print() {}

    template <typename T, typename...Targs>
    inline void print(const T& first, const Targs... args) {
        printSingle(first);
        if (sizeof...(args) != 0) {
            *out << ' ';
            print(args...);
        }
        if (autoflush) {
            flush();
        }
    }

    template <typename...Targs>
    inline void printLine(const Targs... args) {
        print(args...);
        *out << '\n';
        if (autoflush) {
            flush();
        }
    }

    inline void flush() {
        out->flush();
    }

    inline void setPrecision(int digs) {
        *out << fixed << setprecision(digs);
    }
};

Output out(cout, false);
Output err(cerr, true);

#ifdef LOCAL
#define debug(x) err.printLine(#x, '=', x);
#else
#define debug(x)
#endif


const int MOD7 = 1000000007;
const int MOD9 = 1000000009;
const int MODF = 998244353;

int mod = MOD7;

ll gcd(ll a, ll b, ll& x, ll& y) {
    if (a == 0) {
        x = 0;
        y = 1;
        return b;
    }
    int d = gcd(b % a, a, y, x);
    x -= (b / a) * y;
    return d;
}

class modint {
public:
    int n;

    modint() : n(0) {}

    modint(ll n, bool special = false) {
        if (special) {
            this->n = -1;
            return;
        }
        if (n >= 0 && n < mod) {
            this->n = n;
            return;
        }
        n %= mod;
        if (n < 0) {
            n += mod;
        }
        this->n = n;
    }

    modint& operator+=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n += other.n;
        if (n >= mod) {
            n -= mod;
        }
        return *this;
    }

    modint& operator-=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n -= other.n;
        if (n < 0) {
            n += mod;
        }
        return *this;
    }

    modint& operator*=(const modint& other) {
#ifdef LOCAL
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        n = ll(n) * other.n % mod;
        return *this;
    }

    modint& operator/=(const modint& other) {
#ifdef LOCAL
        if (other.n == 0) {
            throw "Division by zero";
        }
        if (n == -1 || other.n == -1) {
            throw "Illegal state";
        }
#endif
        return *this *= other.inverse();
    }

    modint operator-() {
#ifdef LOCAL
        if (n == -1) {
            throw "Illegal state";
        }
#endif
        if (n == 0) {
            return 0;
        }
        return modint(mod - n);
    }

    modint inverse() const {
#ifdef LOCAL
        if (n == -1) {
            throw "Illegal state";
        }
#endif
        ll x, y;
        ll g = gcd(ll(n), ll(mod), x, y);
#ifdef LOCAL
        if (g != 1) {
            throw "not inversable";
        }
#endif
        return x;
    }

    int log(modint alpha);
};

modint nullModint(-1, true);

modint operator+(const modint& a, const modint& b) {
    return modint(a) += b;
}

modint operator-(const modint& a, const modint& b) {
    return modint(a) -= b;
}

modint operator*(const modint& a, const modint& b) {
    return modint(a) *= b;
}

modint operator/(const modint& a, const modint& b) {
    return modint(a) /= b;
}

ostream& operator<<(ostream& out, const modint& v) {
    return out << v.n;
}

bool operator==(const modint& a, const modint& b) {
    return a.n == b.n;
}

bool operator!=(const modint& a, const modint& b) {
    return a.n != b.n;
}

namespace std {
    template <>
    struct hash<modint> {
        size_t operator()(const modint& n) const {
            return n.n;
        }
    };
}

int modint::log(modint alpha) {
#ifdef LOCAL
    if (n == -1 || alpha.n == -1) {
        throw "Illegal state";
    }
#endif
    unordered_map<modint, int> base;
    int exp = 0;
    modint pow = 1;
    modint inv = *this;
    modint alInv = alpha.inverse();
    while (exp * exp < mod) {
        if (inv == 1) {
            return exp;
        }
        base[inv] = exp++;
        pow *= alpha;
        inv *= alInv;
    }
    modint step = pow;
    for (int i = 1;; i++) {
        if (base.count(pow)) {
            return exp * i + base[pow];
        }
        pow *= step;
    }
}


class ETsinshanIDaniel {
public:
    void solve() {
        int n = in.readInt();
        int m = in.readInt();
        arri p, k, b, w;
        in.readArrays(m, p, k, b, w);

        modint seed = 0;
        int base = 0;
        arri t(n);
        arri a(n);
        auto rnd = [&]() -> int {
            int res = seed.n;
            seed = seed * base + 233;
            return res;
        };
        int last = 0;
        for (int i : range(m)) {
            seed = b[i];
            base = w[i];
            for (int j : range(last, p[i])) {
                t[j] = rnd() & 1;
                a[j] = rnd() % k[i] + 1;
            }
            last = p[i];
        }
        ll total1 = 0;
        ll total2 = 0;
        for (int i : range(n)) {
            if (t[i] == 0) {
                total1 += a[i];
            } else {
                total2 += a[i];
            }
        }
        if (total1 > total2) {
            for (int i : range(n)) {
                t[i] = 1 - t[i];
            }
        }
        arri ans(n, 0);
        if (t[0] == 1) {
            ans[0] = 1;
        }
        int at = 0;
        for (int i : range(n)) {
            if (i == at) {
                at++;
                if (at == n) {
                    at = 0;
                }
            }
            if (t[i] == 1) {
                continue;
            }
            ans[i] = a[i];
            int rem = a[i];
            while (rem > 0) {
                while (t[at] == 0 || ans[at] == a[at]) {
                    at++;
                    if (at == n) {
                        at = 0;
                    }
                }
                int cur = min(rem, a[at] - ans[at]);
                ans[at] += cur;
                rem -= cur;
            }
        }
        modint answer = 1;
        for (int i : range(n)) {
            answer *= (ans[i] ^ (ll(i + 1) * (i + 1))) + 1;
        }
        out.printLine(answer);
    }
};


int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
#ifdef LOCAL_RELEASE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    auto time = clock();
#endif
    ETsinshanIDaniel solver;


    solver.solve();
    fflush(stdout);
#ifdef LOCAL_RELEASE
    cerr << setprecision(3) << double(clock() - time) / CLOCKS_PER_SEC << endl;
#endif
    return 0;
}

```