#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(int64_t v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(uint64_t v) {
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(int v) : _m_int(int64_t(v)) {}
  _m_int(unsigned v) : _m_int(uint64_t(v)) {}
  static int inv_mod(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  explicit operator unsigned() const { return val; }
  explicit operator int64_t() const { return val; }
  explicit operator uint64_t() const { return val; }
  explicit operator double() const { return val; }
  explicit operator long double() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val -= MOD - other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return unsigned(x % m);
    unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod(uint64_t(val) * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  friend bool operator==(const _m_int &a, const _m_int &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const _m_int &a, const _m_int &b) {
    return a.val != b.val;
  }
  friend bool operator<(const _m_int &a, const _m_int &b) {
    return a.val < b.val;
  }
  friend bool operator>(const _m_int &a, const _m_int &b) {
    return a.val > b.val;
  }
  friend bool operator<=(const _m_int &a, const _m_int &b) {
    return a.val <= b.val;
  }
  friend bool operator>=(const _m_int &a, const _m_int &b) {
    return a.val >= b.val;
  }
  _m_int inv() const { return inv_mod(val); }
  _m_int pow(int64_t p) const {
    if (p < 0) return inv().pow(-p);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      p >>= 1;
      if (p > 0) a *= a;
    }
    return result;
  }
  friend ostream &operator<<(ostream &os, const _m_int &m) {
    return os << m.val;
  }
};
const int MOD = 1e9 + 7;
using mod_int = _m_int<MOD>;
const int N = 2e6 + 7;
int mu[N];
int lpf[N];
void least_prime_factor() {
  for (int i = 2; i < N; i++) {
    if (!lpf[i]) {
      for (int j = i; j < N; j += i) {
        if (!lpf[j]) lpf[j] = i;
      }
    }
  }
}
void gen_mob() {
  mu[1] = 1;
  for (int i = 2; i < N; i++) {
    if (lpf[i / lpf[i]] == lpf[i])
      mu[i] = 0;
    else
      mu[i] = -1 * mu[i / lpf[i]];
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  least_prime_factor();
  gen_mob();
  int n, k;
  cin >> n >> k;
  vector<mod_int> pw(k + 1);
  vector<mod_int> pr(k + 2);
  for (int i = 1; i <= k; i++) pw[i] = mod_int(i).pow(n);
  mod_int ans = 0;
  for (int i = k; i >= 1; i--) {
    for (int j = i; j <= k; j += i) {
      int l = min(j + i, k + 1);
      pr[j] += mu[i] * pw[j / i];
      pr[l] -= mu[i] * pw[j / i];
    }
  }
  for (int i = 1; i < (int)pr.size() - 1; i++) pr[i + 1] += pr[i];
  for (int i = 1; i <= k; i++) ans += pr[i].val ^ i;
  cout << ans << '\n';
}

### Prompt

Please provide a CPP coded solution to the problem described below:

Let's call an array a of size n coprime iff gcd(a1, a2, ..., an) = 1, where gcd is the greatest common divisor of the arguments.

You are given two numbers n and k. For each i (1 ≤ i ≤ k) you have to determine the number of coprime arrays a of size n such that for every j (1 ≤ j ≤ n) 1 ≤ aj ≤ i. Since the answers can be very large, you have to calculate them modulo 109 + 7.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 2·106) — the size of the desired arrays and the maximum upper bound on elements, respectively.

Output

Since printing 2·106 numbers may take a lot of time, you have to output the answer in such a way:

Let bi be the number of coprime arrays with elements in range [1, i], taken modulo 109 + 7. You have to print <image>, taken modulo 109 + 7. Here <image> denotes bitwise xor operation (^ in C++ or Java, xor in Pascal).

Examples

Input

3 4


Output

82


Input

2000000 8


Output

339310063

Note

Explanation of the example:

Since the number of coprime arrays is large, we will list the arrays that are non-coprime, but contain only elements in range [1, i]:

For i = 1, the only array is coprime. b1 = 1.

For i = 2, array [2, 2, 2] is not coprime. b2 = 7.

For i = 3, arrays [2, 2, 2] and [3, 3, 3] are not coprime. b3 = 25.

For i = 4, arrays [2, 2, 2], [3, 3, 3], [2, 2, 4], [2, 4, 2], [2, 4, 4], [4, 2, 2], [4, 2, 4], [4, 4, 2] and [4, 4, 4] are not coprime. b4 = 55.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pii = pair<int, int>;
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(int64_t v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(uint64_t v) {
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(int v) : _m_int(int64_t(v)) {}
  _m_int(unsigned v) : _m_int(uint64_t(v)) {}
  static int inv_mod(int a, int m = MOD) {
    int g = m, r = a, x = 0, y = 1;
    while (r != 0) {
      int q = g / r;
      g %= r;
      swap(g, r);
      x -= q * y;
      swap(x, y);
    }
    return x < 0 ? x + m : x;
  }
  explicit operator int() const { return val; }
  explicit operator unsigned() const { return val; }
  explicit operator int64_t() const { return val; }
  explicit operator uint64_t() const { return val; }
  explicit operator double() const { return val; }
  explicit operator long double() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val -= MOD - other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return unsigned(x % m);
    unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod(uint64_t(val) * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  friend bool operator==(const _m_int &a, const _m_int &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const _m_int &a, const _m_int &b) {
    return a.val != b.val;
  }
  friend bool operator<(const _m_int &a, const _m_int &b) {
    return a.val < b.val;
  }
  friend bool operator>(const _m_int &a, const _m_int &b) {
    return a.val > b.val;
  }
  friend bool operator<=(const _m_int &a, const _m_int &b) {
    return a.val <= b.val;
  }
  friend bool operator>=(const _m_int &a, const _m_int &b) {
    return a.val >= b.val;
  }
  _m_int inv() const { return inv_mod(val); }
  _m_int pow(int64_t p) const {
    if (p < 0) return inv().pow(-p);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      p >>= 1;
      if (p > 0) a *= a;
    }
    return result;
  }
  friend ostream &operator<<(ostream &os, const _m_int &m) {
    return os << m.val;
  }
};
const int MOD = 1e9 + 7;
using mod_int = _m_int<MOD>;
const int N = 2e6 + 7;
int mu[N];
int lpf[N];
void least_prime_factor() {
  for (int i = 2; i < N; i++) {
    if (!lpf[i]) {
      for (int j = i; j < N; j += i) {
        if (!lpf[j]) lpf[j] = i;
      }
    }
  }
}
void gen_mob() {
  mu[1] = 1;
  for (int i = 2; i < N; i++) {
    if (lpf[i / lpf[i]] == lpf[i])
      mu[i] = 0;
    else
      mu[i] = -1 * mu[i / lpf[i]];
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  least_prime_factor();
  gen_mob();
  int n, k;
  cin >> n >> k;
  vector<mod_int> pw(k + 1);
  vector<mod_int> pr(k + 2);
  for (int i = 1; i <= k; i++) pw[i] = mod_int(i).pow(n);
  mod_int ans = 0;
  for (int i = k; i >= 1; i--) {
    for (int j = i; j <= k; j += i) {
      int l = min(j + i, k + 1);
      pr[j] += mu[i] * pw[j / i];
      pr[l] -= mu[i] * pw[j / i];
    }
  }
  for (int i = 1; i < (int)pr.size() - 1; i++) pr[i + 1] += pr[i];
  for (int i = 1; i <= k; i++) ans += pr[i].val ^ i;
  cout << ans << '\n';
}

```