#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
const int maxn = 4e5 + 400;
int prime[] = {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 poww(long long a, long long b) {
  long long res = 1;
  long long base = a;
  while (b) {
    if (b & 1) {
      res *= base;
      res %= mod;
    }
    base *= base;
    base %= mod;
    b >>= 1;
  }
  return res;
}
struct node {
  int l, r;
  long long mul;
  long long p;
  long long lazy;
  long long lazy2;
} Node[maxn << 2];
void build(int l, int r, int step) {
  Node[step].l = l;
  Node[step].r = r;
  Node[step].mul = Node[step].lazy = 1;
  Node[step].p = Node[step].lazy2 = 0;
  if (l == r) return;
  build(l, (l + r) >> 1, step << 1);
  build(((l + r) >> 1) + 1, r, step << 1 | 1);
}
void push_up(int step) {
  Node[step].mul = Node[step << 1].mul * Node[step << 1 | 1].mul % mod;
  Node[step].p = Node[step << 1].p | Node[step << 1 | 1].p;
}
void push_down(int step) {
  if (Node[step].lazy != 1) {
    Node[step << 1].lazy = Node[step << 1].lazy * Node[step].lazy % mod;
    Node[step << 1].mul =
        Node[step << 1].mul *
        poww(Node[step].lazy, (Node[step << 1].r - Node[step << 1].l + 1)) %
        mod;
    Node[step << 1 | 1].lazy = Node[step << 1 | 1].lazy * Node[step].lazy % mod;
    Node[step << 1 | 1].mul =
        Node[step << 1 | 1].mul *
        poww(Node[step].lazy,
             (Node[step << 1 | 1].r - Node[step << 1 | 1].l + 1)) %
        mod;
    Node[step].lazy = 1;
  }
  if (Node[step].lazy2) {
    Node[step << 1].lazy2 |= Node[step].lazy2;
    Node[step << 1].p |= Node[step].lazy2;
    Node[step << 1 | 1].lazy2 |= Node[step].lazy2;
    Node[step << 1 | 1].p |= Node[step].lazy2;
    Node[step].lazy2 = 0;
  }
}
void update(int l, int r, int step, long long val) {
  if (Node[step].l == l && Node[step].r == r) {
    Node[step].mul = Node[step].mul * poww(val, (r - l + 1)) % mod;
    int vval = val;
    for (int i = 0; prime[i]; i++) {
      while (vval % prime[i] == 0) {
        Node[step].p |= (1ll << i);
        Node[step].lazy2 |= (1ll << i);
        vval /= prime[i];
      }
      if (vval == 1) break;
    }
    Node[step].lazy = Node[step].lazy * val % mod;
    return;
  }
  push_down(step);
  int mid = (Node[step].l + Node[step].r) >> 1;
  if (mid >= r)
    update(l, r, step << 1, val);
  else if (mid < l)
    update(l, r, step << 1 | 1, val);
  else {
    update(l, mid, step << 1, val);
    update(mid + 1, r, step << 1 | 1, val);
  }
  push_up(step);
}
long long qqq = 0;
long long query(int l, int r, int step) {
  if (Node[step].l == l && Node[step].r == r) {
    long long val = Node[step].p;
    long long res = 1;
    qqq |= val;
    res = res * Node[step].mul % mod;
    return res;
  }
  push_down(step);
  int mid = (Node[step].l + Node[step].r) >> 1;
  if (mid >= r)
    return query(l, r, step << 1);
  else if (mid < l)
    return query(l, r, step << 1 | 1);
  else {
    return (query(l, mid, step << 1) * query(mid + 1, r, step << 1 | 1)) % mod;
  }
}
int n, q;
int main() {
  scanf("%d%d", &n, &q);
  build(1, n, 1);
  for (int i = 1; i <= n; i++) {
    long long a;
    scanf("%lld", &a);
    update(i, i, 1, a);
  }
  while (q--) {
    char ss[20];
    scanf("%s", ss);
    if (ss[0] == 'M') {
      int l, r;
      long long val;
      scanf("%d%d%lld", &l, &r, &val);
      update(l, r, 1, val);
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      qqq = 0;
      long long ans = query(l, r, 1);
      int tot = 0;
      while (qqq) {
        if (qqq & 1) {
          ans *= (1 - poww(prime[tot], mod - 2));
          ans %= mod;
        }
        qqq >>= 1;
        tot++;
      }
      ans %= mod;
      ans += mod;
      ans %= mod;
      printf("%lld\n", ans);
    }
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 mod = 1e9 + 7;
const int maxn = 4e5 + 400;
int prime[] = {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 poww(long long a, long long b) {
  long long res = 1;
  long long base = a;
  while (b) {
    if (b & 1) {
      res *= base;
      res %= mod;
    }
    base *= base;
    base %= mod;
    b >>= 1;
  }
  return res;
}
struct node {
  int l, r;
  long long mul;
  long long p;
  long long lazy;
  long long lazy2;
} Node[maxn << 2];
void build(int l, int r, int step) {
  Node[step].l = l;
  Node[step].r = r;
  Node[step].mul = Node[step].lazy = 1;
  Node[step].p = Node[step].lazy2 = 0;
  if (l == r) return;
  build(l, (l + r) >> 1, step << 1);
  build(((l + r) >> 1) + 1, r, step << 1 | 1);
}
void push_up(int step) {
  Node[step].mul = Node[step << 1].mul * Node[step << 1 | 1].mul % mod;
  Node[step].p = Node[step << 1].p | Node[step << 1 | 1].p;
}
void push_down(int step) {
  if (Node[step].lazy != 1) {
    Node[step << 1].lazy = Node[step << 1].lazy * Node[step].lazy % mod;
    Node[step << 1].mul =
        Node[step << 1].mul *
        poww(Node[step].lazy, (Node[step << 1].r - Node[step << 1].l + 1)) %
        mod;
    Node[step << 1 | 1].lazy = Node[step << 1 | 1].lazy * Node[step].lazy % mod;
    Node[step << 1 | 1].mul =
        Node[step << 1 | 1].mul *
        poww(Node[step].lazy,
             (Node[step << 1 | 1].r - Node[step << 1 | 1].l + 1)) %
        mod;
    Node[step].lazy = 1;
  }
  if (Node[step].lazy2) {
    Node[step << 1].lazy2 |= Node[step].lazy2;
    Node[step << 1].p |= Node[step].lazy2;
    Node[step << 1 | 1].lazy2 |= Node[step].lazy2;
    Node[step << 1 | 1].p |= Node[step].lazy2;
    Node[step].lazy2 = 0;
  }
}
void update(int l, int r, int step, long long val) {
  if (Node[step].l == l && Node[step].r == r) {
    Node[step].mul = Node[step].mul * poww(val, (r - l + 1)) % mod;
    int vval = val;
    for (int i = 0; prime[i]; i++) {
      while (vval % prime[i] == 0) {
        Node[step].p |= (1ll << i);
        Node[step].lazy2 |= (1ll << i);
        vval /= prime[i];
      }
      if (vval == 1) break;
    }
    Node[step].lazy = Node[step].lazy * val % mod;
    return;
  }
  push_down(step);
  int mid = (Node[step].l + Node[step].r) >> 1;
  if (mid >= r)
    update(l, r, step << 1, val);
  else if (mid < l)
    update(l, r, step << 1 | 1, val);
  else {
    update(l, mid, step << 1, val);
    update(mid + 1, r, step << 1 | 1, val);
  }
  push_up(step);
}
long long qqq = 0;
long long query(int l, int r, int step) {
  if (Node[step].l == l && Node[step].r == r) {
    long long val = Node[step].p;
    long long res = 1;
    qqq |= val;
    res = res * Node[step].mul % mod;
    return res;
  }
  push_down(step);
  int mid = (Node[step].l + Node[step].r) >> 1;
  if (mid >= r)
    return query(l, r, step << 1);
  else if (mid < l)
    return query(l, r, step << 1 | 1);
  else {
    return (query(l, mid, step << 1) * query(mid + 1, r, step << 1 | 1)) % mod;
  }
}
int n, q;
int main() {
  scanf("%d%d", &n, &q);
  build(1, n, 1);
  for (int i = 1; i <= n; i++) {
    long long a;
    scanf("%lld", &a);
    update(i, i, 1, a);
  }
  while (q--) {
    char ss[20];
    scanf("%s", ss);
    if (ss[0] == 'M') {
      int l, r;
      long long val;
      scanf("%d%d%lld", &l, &r, &val);
      update(l, r, 1, val);
    } else {
      int l, r;
      scanf("%d%d", &l, &r);
      qqq = 0;
      long long ans = query(l, r, 1);
      int tot = 0;
      while (qqq) {
        if (qqq & 1) {
          ans *= (1 - poww(prime[tot], mod - 2));
          ans %= mod;
        }
        qqq >>= 1;
        tot++;
      }
      ans %= mod;
      ans += mod;
      ans %= mod;
      printf("%lld\n", ans);
    }
  }
}

```