#include <bits/stdc++.h>
using namespace std;
const int MAXN = 4e5 + 5;
const int MOD = 1e9 + 7;
const int MAXP = 62;
const int MAXV = 301;
int a[MAXN], N, Q;
int inv[MAXP];
long long M[MAXV];
int pr[] = {2,   3,   5,   7,   11,  13,  17,  19,  23,  29,  31,  37,  41,
            43,  47,  53,  59,  61,  67,  71,  73,  79,  83,  89,  97,  101,
            103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
            173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239,
            241, 251, 257, 263, 269, 271, 277, 281, 283, 293};
long long Power(int a, int n) {
  long long res = 1;
  while (n) {
    if (n & 1LL) res = (1LL * res * a) % MOD;
    n >>= 1LL;
    a = (1LL * a * a) % MOD;
  }
  return res;
}
long long Mul(int a, int b) { return (1LL * a * b) % MOD; }
void Prepare() {
  for (int i = 0; i < MAXP; ++i) inv[i] = Power(pr[i], MOD - 2);
  for (int i = 1; i < MAXV; ++i) {
    for (int k = 0; k < MAXP; ++k) {
      if (i % pr[k] == 0) {
        M[i] |= (1LL << k);
      }
    }
  }
}
struct SegmentTree_Product {
  vector<int> Node, Lazy;
  void Init(int n) {
    Node.resize(4 * n + 1);
    Lazy.resize(4 * n + 1);
    for (int i = 1; i <= 4 * n; ++i) Lazy[i] = 1, Node[i] = 1;
  }
  void Build(int k, int left, int right) {
    if (left == right) {
      Node[k] = a[left];
    }
    int mid = (left + right) / 2;
    Build(k << 1, left, mid);
    Build(k << 1 | 1, mid + 1, right);
    Node[k] = Mul(Node[k << 1], Node[k << 1 | 1]);
  }
  void Push_down(int k, int left, int right) {
    if (Lazy[k] != 1) {
      Node[k] = Mul(Node[k], Power(Lazy[k], (right - left + 1)));
      if (left != right) {
        Lazy[k << 1] = Mul(Lazy[k << 1], Lazy[k]);
        Lazy[k << 1 | 1] = Mul(Lazy[k << 1 | 1], Lazy[k]);
      }
    }
    Lazy[k] = 1;
  }
  void Update(int k, int left, int right, int u, int v, int p) {
    Push_down(k, left, right);
    if (right < u || v < left) return;
    if (u <= left && right <= v) {
      Lazy[k] = Mul(Lazy[k], p);
      Push_down(k, left, right);
      return;
    }
    int mid = (left + right) / 2;
    Update(k << 1, left, mid, u, v, p);
    Update(k << 1 | 1, mid + 1, right, u, v, p);
    Node[k] = Mul(Node[k << 1], Node[k << 1 | 1]);
  }
  long long Query(int k, int left, int right, int u, int v) {
    Push_down(k, left, right);
    if (right < u || v < left) return 1;
    if (u <= left && right <= v) {
      return Node[k];
    }
    int mid = (left + right) / 2;
    return (1LL * Query(k << 1, left, mid, u, v) *
            Query(k << 1 | 1, mid + 1, right, u, v)) %
           MOD;
  }
};
struct SegmentTree_Bool {
  vector<long long> Node, Lazy;
  void Init(int n) {
    Node.resize(4 * n + 1);
    Lazy.resize(4 * n + 1);
  }
  void Push_down(int k, int left, int right) {
    if (Lazy[k] != 0) {
      Node[k] = Node[k] | Lazy[k];
      if (left != right) {
        Lazy[k << 1] |= Lazy[k];
        Lazy[k << 1 | 1] |= Lazy[k];
      }
    }
    Lazy[k] = 0;
  }
  void Update(int k, int left, int right, int u, int v, long long p) {
    Push_down(k, left, right);
    if (right < u || v < left) return;
    if (u <= left && right <= v) {
      Lazy[k] |= p;
      Push_down(k, left, right);
      return;
    }
    int mid = (left + right) / 2;
    Update(k << 1, left, mid, u, v, p);
    Update(k << 1 | 1, mid + 1, right, u, v, p);
    Node[k] = (Node[k << 1] | Node[k << 1 | 1]);
  }
  long long Query(int k, int left, int right, int u, int v) {
    Push_down(k, left, right);
    if (right < u || v < left) return 0;
    if (u <= left && right <= v) {
      return Node[k];
    }
    int mid = (left + right) / 2;
    return (Query(k << 1, left, mid, u, v) |
            Query(k << 1 | 1, mid + 1, right, u, v));
  }
};
SegmentTree_Bool BoolTree;
SegmentTree_Product ProductTree;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> N >> Q;
  Prepare();
  for (int i = 1; i <= N; ++i) cin >> a[i];
  BoolTree.Init(N);
  ProductTree.Init(N);
  for (int i = 1; i <= N; ++i) {
    BoolTree.Update(1, 1, N, i, i, M[a[i]]);
    ProductTree.Update(1, 1, N, i, i, a[i]);
  }
  while (Q--) {
    string op;
    cin >> op;
    if (op[0] == 'T') {
      int left, right;
      cin >> left >> right;
      long long ans = ProductTree.Query(1, 1, N, left, right);
      long long Mask = BoolTree.Query(1, 1, N, left, right);
      for (int i = 0; i < MAXP; ++i) {
        if ((Mask >> i) & 1) {
          ans = Mul(ans, pr[i] - 1);
          ans = Mul(ans, inv[i]);
        }
      }
      cout << ans << endl;
    } else {
      int left, right, value;
      cin >> left >> right >> value;
      ProductTree.Update(1, 1, N, left, right, value);
      BoolTree.Update(1, 1, N, left, right, M[value]);
    }
  }
  return 0;
}

### Prompt

In Cpp, your task is to solve the following problem:

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;
const int MAXN = 4e5 + 5;
const int MOD = 1e9 + 7;
const int MAXP = 62;
const int MAXV = 301;
int a[MAXN], N, Q;
int inv[MAXP];
long long M[MAXV];
int pr[] = {2,   3,   5,   7,   11,  13,  17,  19,  23,  29,  31,  37,  41,
            43,  47,  53,  59,  61,  67,  71,  73,  79,  83,  89,  97,  101,
            103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
            173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239,
            241, 251, 257, 263, 269, 271, 277, 281, 283, 293};
long long Power(int a, int n) {
  long long res = 1;
  while (n) {
    if (n & 1LL) res = (1LL * res * a) % MOD;
    n >>= 1LL;
    a = (1LL * a * a) % MOD;
  }
  return res;
}
long long Mul(int a, int b) { return (1LL * a * b) % MOD; }
void Prepare() {
  for (int i = 0; i < MAXP; ++i) inv[i] = Power(pr[i], MOD - 2);
  for (int i = 1; i < MAXV; ++i) {
    for (int k = 0; k < MAXP; ++k) {
      if (i % pr[k] == 0) {
        M[i] |= (1LL << k);
      }
    }
  }
}
struct SegmentTree_Product {
  vector<int> Node, Lazy;
  void Init(int n) {
    Node.resize(4 * n + 1);
    Lazy.resize(4 * n + 1);
    for (int i = 1; i <= 4 * n; ++i) Lazy[i] = 1, Node[i] = 1;
  }
  void Build(int k, int left, int right) {
    if (left == right) {
      Node[k] = a[left];
    }
    int mid = (left + right) / 2;
    Build(k << 1, left, mid);
    Build(k << 1 | 1, mid + 1, right);
    Node[k] = Mul(Node[k << 1], Node[k << 1 | 1]);
  }
  void Push_down(int k, int left, int right) {
    if (Lazy[k] != 1) {
      Node[k] = Mul(Node[k], Power(Lazy[k], (right - left + 1)));
      if (left != right) {
        Lazy[k << 1] = Mul(Lazy[k << 1], Lazy[k]);
        Lazy[k << 1 | 1] = Mul(Lazy[k << 1 | 1], Lazy[k]);
      }
    }
    Lazy[k] = 1;
  }
  void Update(int k, int left, int right, int u, int v, int p) {
    Push_down(k, left, right);
    if (right < u || v < left) return;
    if (u <= left && right <= v) {
      Lazy[k] = Mul(Lazy[k], p);
      Push_down(k, left, right);
      return;
    }
    int mid = (left + right) / 2;
    Update(k << 1, left, mid, u, v, p);
    Update(k << 1 | 1, mid + 1, right, u, v, p);
    Node[k] = Mul(Node[k << 1], Node[k << 1 | 1]);
  }
  long long Query(int k, int left, int right, int u, int v) {
    Push_down(k, left, right);
    if (right < u || v < left) return 1;
    if (u <= left && right <= v) {
      return Node[k];
    }
    int mid = (left + right) / 2;
    return (1LL * Query(k << 1, left, mid, u, v) *
            Query(k << 1 | 1, mid + 1, right, u, v)) %
           MOD;
  }
};
struct SegmentTree_Bool {
  vector<long long> Node, Lazy;
  void Init(int n) {
    Node.resize(4 * n + 1);
    Lazy.resize(4 * n + 1);
  }
  void Push_down(int k, int left, int right) {
    if (Lazy[k] != 0) {
      Node[k] = Node[k] | Lazy[k];
      if (left != right) {
        Lazy[k << 1] |= Lazy[k];
        Lazy[k << 1 | 1] |= Lazy[k];
      }
    }
    Lazy[k] = 0;
  }
  void Update(int k, int left, int right, int u, int v, long long p) {
    Push_down(k, left, right);
    if (right < u || v < left) return;
    if (u <= left && right <= v) {
      Lazy[k] |= p;
      Push_down(k, left, right);
      return;
    }
    int mid = (left + right) / 2;
    Update(k << 1, left, mid, u, v, p);
    Update(k << 1 | 1, mid + 1, right, u, v, p);
    Node[k] = (Node[k << 1] | Node[k << 1 | 1]);
  }
  long long Query(int k, int left, int right, int u, int v) {
    Push_down(k, left, right);
    if (right < u || v < left) return 0;
    if (u <= left && right <= v) {
      return Node[k];
    }
    int mid = (left + right) / 2;
    return (Query(k << 1, left, mid, u, v) |
            Query(k << 1 | 1, mid + 1, right, u, v));
  }
};
SegmentTree_Bool BoolTree;
SegmentTree_Product ProductTree;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> N >> Q;
  Prepare();
  for (int i = 1; i <= N; ++i) cin >> a[i];
  BoolTree.Init(N);
  ProductTree.Init(N);
  for (int i = 1; i <= N; ++i) {
    BoolTree.Update(1, 1, N, i, i, M[a[i]]);
    ProductTree.Update(1, 1, N, i, i, a[i]);
  }
  while (Q--) {
    string op;
    cin >> op;
    if (op[0] == 'T') {
      int left, right;
      cin >> left >> right;
      long long ans = ProductTree.Query(1, 1, N, left, right);
      long long Mask = BoolTree.Query(1, 1, N, left, right);
      for (int i = 0; i < MAXP; ++i) {
        if ((Mask >> i) & 1) {
          ans = Mul(ans, pr[i] - 1);
          ans = Mul(ans, inv[i]);
        }
      }
      cout << ans << endl;
    } else {
      int left, right, value;
      cin >> left >> right >> value;
      ProductTree.Update(1, 1, N, left, right, value);
      BoolTree.Update(1, 1, N, left, right, M[value]);
    }
  }
  return 0;
}

```