#include <bits/stdc++.h>
using namespace std;
long long read() {
  long long sum = 0, fh = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') fh = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    sum = (sum << 3) + (sum << 1) + (ch ^ 48);
    ch = getchar();
  }
  return sum * fh;
}
long long a[400010];
long long P[400];
long long tot = 0;
bool e[400];
long long inv[400];
long long qpow(long long x, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = ans * x % 1000000007;
    x = x * x % 1000000007;
    b >>= 1;
  }
  return ans;
}
void sieve(long long n) {
  e[1] = 1;
  for (long long i = 2; i <= n; ++i) {
    if (!e[i]) {
      P[++tot] = i;
    }
    for (long long j = 1; j <= tot; ++j) {
      if (P[j] * i > n) break;
      e[P[j] * i] = 1;
      if (i % P[j] == 0) break;
    }
  }
  for (long long i = 1; i <= tot; ++i) {
    inv[i] = (P[i] - 1) * qpow(P[i], 1000000007 - 2) % 1000000007;
  }
}
long long BIT(long long x) {
  long long ans = 0;
  for (long long i = 1; i <= tot; ++i) {
    if (!(x % P[i])) {
      ans += (1ll << (i - 1));
    }
  }
  return ans;
}
char ch[10];
long long tag[400010 * 4];
long long Or[400010 * 4];
long long mul[400010 * 4];
long long tagmul[400010 * 4];
void upd(long long p) {
  mul[p] = mul[p << 1] * mul[p << 1 | 1] % 1000000007;
  Or[p] = Or[p << 1] | Or[p << 1 | 1];
}
void pd(long long p, long long l, long long r) {
  long long mid = l + r >> 1;
  tag[p << 1] |= tag[p];
  tag[p << 1 | 1] |= tag[p];
  Or[p << 1] |= tag[p];
  Or[p << 1 | 1] |= tag[p];
  tagmul[p << 1] = tagmul[p << 1] * tagmul[p] % 1000000007;
  tagmul[p << 1 | 1] = tagmul[p << 1 | 1] * tagmul[p] % 1000000007;
  mul[p << 1] = mul[p << 1] * qpow(tagmul[p], mid - l + 1) % 1000000007;
  mul[p << 1 | 1] = mul[p << 1 | 1] * qpow(tagmul[p], r - mid) % 1000000007;
  tag[p] = 0;
  tagmul[p] = 1;
  return;
}
void ins(long long p, long long l, long long r, long long x, long long v,
         long long M) {
  tagmul[p] = 1;
  if (l == r) {
    Or[p] = v;
    mul[p] = M;
    return;
  }
  long long mid = l + r >> 1;
  if (x <= mid)
    ins(p << 1, l, mid, x, v, M);
  else
    ins(p << 1 | 1, mid + 1, r, x, v, M);
  upd(p);
}
void modify(long long p, long long l, long long r, long long L, long long R,
            long long v, long long M) {
  if (L <= l && R >= r) {
    mul[p] = mul[p] * qpow(M, r - l + 1) % 1000000007;
    tagmul[p] = tagmul[p] * M % 1000000007;
    Or[p] |= v;
    tag[p] |= v;
    return;
  }
  if (tag[p] || tagmul[p] != 1) pd(p, l, r);
  long long mid = l + r >> 1;
  if (L <= mid) modify(p << 1, l, mid, L, R, v, M);
  if (R > mid) modify(p << 1 | 1, mid + 1, r, L, R, v, M);
  upd(p);
}
long long query(long long p, long long l, long long r, long long L, long long R,
                long long &M) {
  if (L <= l && R >= r) {
    M = mul[p];
    return Or[p];
  }
  if (tag[p] || tagmul[p] != 1) pd(p, l, r);
  long long mid = l + r >> 1;
  long long m1 = 1, m2 = 1;
  long long ans = 0;
  if (L <= mid) ans |= query(p << 1, l, mid, L, R, m1);
  if (R > mid) ans |= query(p << 1 | 1, mid + 1, r, L, R, m2);
  upd(p);
  M = m1 * m2 % 1000000007;
  return ans;
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n = read(), Q = read();
  sieve(300);
  for (long long i = 1; i <= n; ++i) {
    a[i] = read();
    ins(1, 1, n, i, BIT(a[i]), a[i]);
  }
  while (Q--) {
    scanf("%s", ch);
    if (ch[0] == 'M') {
      long long l = read(), r = read(), x = read();
      modify(1, 1, n, l, r, BIT(x), x);
    }
    if (ch[0] == 'T') {
      long long l = read(), r = read();
      long long MUL = 1;
      long long x = query(1, 1, n, l, r, MUL);
      for (long long i = 1; i <= tot; ++i) {
        if ((1ll << (i - 1)) & x) {
          MUL = MUL * inv[i] % 1000000007;
        }
      }
      printf("%lld\n", MUL);
    }
  }
  return 0;
}

### 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;
long long read() {
  long long sum = 0, fh = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') fh = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    sum = (sum << 3) + (sum << 1) + (ch ^ 48);
    ch = getchar();
  }
  return sum * fh;
}
long long a[400010];
long long P[400];
long long tot = 0;
bool e[400];
long long inv[400];
long long qpow(long long x, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = ans * x % 1000000007;
    x = x * x % 1000000007;
    b >>= 1;
  }
  return ans;
}
void sieve(long long n) {
  e[1] = 1;
  for (long long i = 2; i <= n; ++i) {
    if (!e[i]) {
      P[++tot] = i;
    }
    for (long long j = 1; j <= tot; ++j) {
      if (P[j] * i > n) break;
      e[P[j] * i] = 1;
      if (i % P[j] == 0) break;
    }
  }
  for (long long i = 1; i <= tot; ++i) {
    inv[i] = (P[i] - 1) * qpow(P[i], 1000000007 - 2) % 1000000007;
  }
}
long long BIT(long long x) {
  long long ans = 0;
  for (long long i = 1; i <= tot; ++i) {
    if (!(x % P[i])) {
      ans += (1ll << (i - 1));
    }
  }
  return ans;
}
char ch[10];
long long tag[400010 * 4];
long long Or[400010 * 4];
long long mul[400010 * 4];
long long tagmul[400010 * 4];
void upd(long long p) {
  mul[p] = mul[p << 1] * mul[p << 1 | 1] % 1000000007;
  Or[p] = Or[p << 1] | Or[p << 1 | 1];
}
void pd(long long p, long long l, long long r) {
  long long mid = l + r >> 1;
  tag[p << 1] |= tag[p];
  tag[p << 1 | 1] |= tag[p];
  Or[p << 1] |= tag[p];
  Or[p << 1 | 1] |= tag[p];
  tagmul[p << 1] = tagmul[p << 1] * tagmul[p] % 1000000007;
  tagmul[p << 1 | 1] = tagmul[p << 1 | 1] * tagmul[p] % 1000000007;
  mul[p << 1] = mul[p << 1] * qpow(tagmul[p], mid - l + 1) % 1000000007;
  mul[p << 1 | 1] = mul[p << 1 | 1] * qpow(tagmul[p], r - mid) % 1000000007;
  tag[p] = 0;
  tagmul[p] = 1;
  return;
}
void ins(long long p, long long l, long long r, long long x, long long v,
         long long M) {
  tagmul[p] = 1;
  if (l == r) {
    Or[p] = v;
    mul[p] = M;
    return;
  }
  long long mid = l + r >> 1;
  if (x <= mid)
    ins(p << 1, l, mid, x, v, M);
  else
    ins(p << 1 | 1, mid + 1, r, x, v, M);
  upd(p);
}
void modify(long long p, long long l, long long r, long long L, long long R,
            long long v, long long M) {
  if (L <= l && R >= r) {
    mul[p] = mul[p] * qpow(M, r - l + 1) % 1000000007;
    tagmul[p] = tagmul[p] * M % 1000000007;
    Or[p] |= v;
    tag[p] |= v;
    return;
  }
  if (tag[p] || tagmul[p] != 1) pd(p, l, r);
  long long mid = l + r >> 1;
  if (L <= mid) modify(p << 1, l, mid, L, R, v, M);
  if (R > mid) modify(p << 1 | 1, mid + 1, r, L, R, v, M);
  upd(p);
}
long long query(long long p, long long l, long long r, long long L, long long R,
                long long &M) {
  if (L <= l && R >= r) {
    M = mul[p];
    return Or[p];
  }
  if (tag[p] || tagmul[p] != 1) pd(p, l, r);
  long long mid = l + r >> 1;
  long long m1 = 1, m2 = 1;
  long long ans = 0;
  if (L <= mid) ans |= query(p << 1, l, mid, L, R, m1);
  if (R > mid) ans |= query(p << 1 | 1, mid + 1, r, L, R, m2);
  upd(p);
  M = m1 * m2 % 1000000007;
  return ans;
}
signed main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n = read(), Q = read();
  sieve(300);
  for (long long i = 1; i <= n; ++i) {
    a[i] = read();
    ins(1, 1, n, i, BIT(a[i]), a[i]);
  }
  while (Q--) {
    scanf("%s", ch);
    if (ch[0] == 'M') {
      long long l = read(), r = read(), x = read();
      modify(1, 1, n, l, r, BIT(x), x);
    }
    if (ch[0] == 'T') {
      long long l = read(), r = read();
      long long MUL = 1;
      long long x = query(1, 1, n, l, r, MUL);
      for (long long i = 1; i <= tot; ++i) {
        if ((1ll << (i - 1)) & x) {
          MUL = MUL * inv[i] % 1000000007;
        }
      }
      printf("%lld\n", MUL);
    }
  }
  return 0;
}

```