#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
template <class T>
bool set_max(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool set_min(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename... Args>
void readln(Args &...args) {
  ((cin >> args), ...);
}
template <typename... Args>
void writeln(Args... args) {
  ((cout << args << " "), ...);
}
template <typename T, typename... Args>
void push_to_vec(vector<T> &v, Args &&...args) {
  (v.push_back(forward<Args>(args)), ...);
}
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename T>
string to_string(T v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const int N = 1e6 + 10;
const int MOD = 1e9 + 7;
vector<int> primes;
vector<int> inverse_primes;
ll fast_power(ll a, ll p) {
  ll ans = 1;
  while (p) {
    if (p % 2) {
      ans = ans * a % MOD;
    }
    a = a * a % MOD;
    p /= 2;
  }
  return ans;
}
ull get_mask(ull value) {
  ull mask = 0;
  for (std::size_t i = 0; i < primes.size(); i++) {
    if (value % primes[i] == 0) {
      mask |= 1ull << i;
    }
  }
  return mask;
}
struct Lazy_Context {
  Lazy_Context() : value(1), mask(0) {}
  Lazy_Context(ull value, ull mask) : value(value), mask(mask) {}
  void operator+=(const Lazy_Context &lc) {
    value = value * lc.value % MOD;
    mask |= lc.mask;
  }
  ull value;
  ull mask;
};
struct Node {
  Node() {
    value = 1;
    mask = 0;
    size = 0;
  }
  Node(int v) {
    value = static_cast<ull>(v);
    mask = get_mask(v);
    size = 1;
  }
  Node(const Node &l, const Node &r) {
    value = l.value * r.value % MOD;
    mask = l.mask | r.mask;
    size = l.size + r.size;
  }
  void apply(Lazy_Context lz) {
    value = value * fast_power(lz.value, size) % MOD;
    mask |= lz.mask;
  }
  ull get_ans() {
    ll ans = value;
    for (std::size_t j = 0; j < primes.size(); j++) {
      if ((mask >> j) & 1u) {
        ans = ans * inverse_primes[j] % MOD;
      }
    }
    return ans;
  }

 private:
  ull value;
  ull mask;
  std::size_t size;
};
template <class Node, class Value, class lazy_count = int>
class SegmentTree {
 public:
  explicit SegmentTree(vector<Value> &base) {
    n = base.size();
    height = 0;
    while ((1u << static_cast<std::size_t>(height)) < n) {
      height++;
    }
    tree.resize(n * 2);
    is_dirty.assign(n, false);
    lazy.resize(n);
    for (int i = 0; i < n; i++) {
      tree[i + n] = Node(base[i]);
    }
    for (int i = n - 1; i > 0; i--) {
      tree[i] = Node(tree[i * 2], tree[i * 2 + 1]);
      lazy[i] = lazy_count();
    }
  }
  Node query(int l, int r) {
    if (l >= r) {
      return Node();
    }
    l += n, r += n;
    push(l), push(r - 1);
    Node lp, rp;
    while (l < r) {
      if (l % 2) {
        lp = Node(lp, tree[l]);
        l++;
      }
      if (r % 2) {
        r--;
        rp = Node(tree[r], rp);
      }
      l /= 2, r /= 2;
    }
    return Node(lp, rp);
  }
  void update(int l, int r, Lazy_Context lc) {
    if (l >= r) {
      return;
    }
    l += n, r += n;
    push(l), push(r - 1);
    int l0 = l, r0 = r;
    while (l < r) {
      if (l % 2) {
        apply(l, lc);
        l++;
      }
      if (r % 2) {
        r--;
        apply(r, lc);
      }
      l /= 2, r /= 2;
    }
    build(l0), build(r0 - 1);
  }

 private:
  int n, height;
  vector<bool> is_dirty;
  vector<Node> tree;
  vector<lazy_count> lazy;
  void apply(int x, const Lazy_Context &lc) {
    tree[x].apply(lc);
    if (x < n) {
      is_dirty[x] = true;
      lazy[x] += lc;
    }
  }
  void push(int x) {
    for (std::size_t h = height; h > 0; h--) {
      int i = static_cast<uint32_t>(x) >> h;
      if (is_dirty[i]) {
        apply(i * 2, lazy[i]);
        apply(i * 2 + 1, lazy[i]);
        lazy[i] = Lazy_Context();
        is_dirty[i] = false;
      }
    }
  }
  void build(int x) {
    for (x /= 2; x > 0; x /= 2) {
      tree[x] = Node(tree[x * 2], tree[x * 2 + 1]);
      if (is_dirty[x]) {
        tree[x].apply(lazy[x]);
      }
    }
  }
};
int main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  vector<bool> is_prime(350, true);
  for (int i = 2; i <= 300; i++) {
    if (is_prime[i]) {
      primes.push_back(i);
    }
    for (int j : primes) {
      int k = j * i;
      if (k < 350) {
        is_prime[k] = false;
      }
    }
  }
  for (int j : primes) {
    inverse_primes.push_back(fast_power(j, MOD - 2) * (j - 1) % MOD);
  }
  int n, q;
  cin >> n >> q;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  SegmentTree<Node, int, Lazy_Context> tree(a);
  while (q--) {
    string str;
    cin >> str;
    if (str[0] == 'T') {
      int l, r;
      cin >> l >> r;
      cout << tree.query(l - 1, r).get_ans() << endl;
    } else {
      int l, r, v;
      cin >> l >> r >> v;
      tree.update(l - 1, r, Lazy_Context(v, get_mask(v)));
    }
  }
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

You are given an array a_1, a_2, …, a_n.

You need to perform q queries of the following two types:

  1. "MULTIPLY l r x" — for every i (l ≤ i ≤ r) multiply a_i by x.
  2. "TOTIENT l r" — print \varphi(∏ _{i=l}^{r} a_i) taken modulo 10^9+7, where \varphi denotes Euler's totient function. 



The [Euler's totient function](http://gg.gg/euler_totient) of a positive integer n (denoted as \varphi(n)) is the number of integers x (1 ≤ x ≤ n) such that \gcd(n,x) = 1.

Input

The first line contains two integers n and q (1 ≤ n ≤ 4 ⋅ 10^5, 1 ≤ q ≤ 2 ⋅ 10^5) — the number of elements in array a and the number of queries.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 300) — the elements of array a.

Then q lines follow, describing queries in the format given in the statement.

  1. "MULTIPLY l r x" (1 ≤ l ≤ r ≤ n, 1 ≤ x ≤ 300) — denotes a multiplication query.
  2. "TOTIENT l r" (1 ≤ l ≤ r ≤ n) — denotes a query on the value of Euler's totient function. 



It is guaranteed that there is at least one "TOTIENT" query.

Output

For each "TOTIENT" query, print the answer to it.

Example

Input

4 4
5 9 1 2
TOTIENT 3 3
TOTIENT 3 4
MULTIPLY 4 4 3
TOTIENT 4 4


Output

1
1
2

Note

In the first example, \varphi(1) = 1 for the first query, \varphi(2) = 1 for the second query and \varphi(6) = 2 for the third one.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
template <class T>
bool set_max(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
bool set_min(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <typename... Args>
void readln(Args &...args) {
  ((cin >> args), ...);
}
template <typename... Args>
void writeln(Args... args) {
  ((cout << args << " "), ...);
}
template <typename T, typename... Args>
void push_to_vec(vector<T> &v, Args &&...args) {
  (v.push_back(forward<Args>(args)), ...);
}
string to_string(const string &s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename T>
string to_string(T v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
const int N = 1e6 + 10;
const int MOD = 1e9 + 7;
vector<int> primes;
vector<int> inverse_primes;
ll fast_power(ll a, ll p) {
  ll ans = 1;
  while (p) {
    if (p % 2) {
      ans = ans * a % MOD;
    }
    a = a * a % MOD;
    p /= 2;
  }
  return ans;
}
ull get_mask(ull value) {
  ull mask = 0;
  for (std::size_t i = 0; i < primes.size(); i++) {
    if (value % primes[i] == 0) {
      mask |= 1ull << i;
    }
  }
  return mask;
}
struct Lazy_Context {
  Lazy_Context() : value(1), mask(0) {}
  Lazy_Context(ull value, ull mask) : value(value), mask(mask) {}
  void operator+=(const Lazy_Context &lc) {
    value = value * lc.value % MOD;
    mask |= lc.mask;
  }
  ull value;
  ull mask;
};
struct Node {
  Node() {
    value = 1;
    mask = 0;
    size = 0;
  }
  Node(int v) {
    value = static_cast<ull>(v);
    mask = get_mask(v);
    size = 1;
  }
  Node(const Node &l, const Node &r) {
    value = l.value * r.value % MOD;
    mask = l.mask | r.mask;
    size = l.size + r.size;
  }
  void apply(Lazy_Context lz) {
    value = value * fast_power(lz.value, size) % MOD;
    mask |= lz.mask;
  }
  ull get_ans() {
    ll ans = value;
    for (std::size_t j = 0; j < primes.size(); j++) {
      if ((mask >> j) & 1u) {
        ans = ans * inverse_primes[j] % MOD;
      }
    }
    return ans;
  }

 private:
  ull value;
  ull mask;
  std::size_t size;
};
template <class Node, class Value, class lazy_count = int>
class SegmentTree {
 public:
  explicit SegmentTree(vector<Value> &base) {
    n = base.size();
    height = 0;
    while ((1u << static_cast<std::size_t>(height)) < n) {
      height++;
    }
    tree.resize(n * 2);
    is_dirty.assign(n, false);
    lazy.resize(n);
    for (int i = 0; i < n; i++) {
      tree[i + n] = Node(base[i]);
    }
    for (int i = n - 1; i > 0; i--) {
      tree[i] = Node(tree[i * 2], tree[i * 2 + 1]);
      lazy[i] = lazy_count();
    }
  }
  Node query(int l, int r) {
    if (l >= r) {
      return Node();
    }
    l += n, r += n;
    push(l), push(r - 1);
    Node lp, rp;
    while (l < r) {
      if (l % 2) {
        lp = Node(lp, tree[l]);
        l++;
      }
      if (r % 2) {
        r--;
        rp = Node(tree[r], rp);
      }
      l /= 2, r /= 2;
    }
    return Node(lp, rp);
  }
  void update(int l, int r, Lazy_Context lc) {
    if (l >= r) {
      return;
    }
    l += n, r += n;
    push(l), push(r - 1);
    int l0 = l, r0 = r;
    while (l < r) {
      if (l % 2) {
        apply(l, lc);
        l++;
      }
      if (r % 2) {
        r--;
        apply(r, lc);
      }
      l /= 2, r /= 2;
    }
    build(l0), build(r0 - 1);
  }

 private:
  int n, height;
  vector<bool> is_dirty;
  vector<Node> tree;
  vector<lazy_count> lazy;
  void apply(int x, const Lazy_Context &lc) {
    tree[x].apply(lc);
    if (x < n) {
      is_dirty[x] = true;
      lazy[x] += lc;
    }
  }
  void push(int x) {
    for (std::size_t h = height; h > 0; h--) {
      int i = static_cast<uint32_t>(x) >> h;
      if (is_dirty[i]) {
        apply(i * 2, lazy[i]);
        apply(i * 2 + 1, lazy[i]);
        lazy[i] = Lazy_Context();
        is_dirty[i] = false;
      }
    }
  }
  void build(int x) {
    for (x /= 2; x > 0; x /= 2) {
      tree[x] = Node(tree[x * 2], tree[x * 2 + 1]);
      if (is_dirty[x]) {
        tree[x].apply(lazy[x]);
      }
    }
  }
};
int main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  vector<bool> is_prime(350, true);
  for (int i = 2; i <= 300; i++) {
    if (is_prime[i]) {
      primes.push_back(i);
    }
    for (int j : primes) {
      int k = j * i;
      if (k < 350) {
        is_prime[k] = false;
      }
    }
  }
  for (int j : primes) {
    inverse_primes.push_back(fast_power(j, MOD - 2) * (j - 1) % MOD);
  }
  int n, q;
  cin >> n >> q;
  vector<int> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  SegmentTree<Node, int, Lazy_Context> tree(a);
  while (q--) {
    string str;
    cin >> str;
    if (str[0] == 'T') {
      int l, r;
      cin >> l >> r;
      cout << tree.query(l - 1, r).get_ans() << endl;
    } else {
      int l, r, v;
      cin >> l >> r >> v;
      tree.update(l - 1, r, Lazy_Context(v, get_mask(v)));
    }
  }
  return 0;
}

```