#include <bits/stdc++.h>
const int N = 4e5 + 5, M = 301, M2 = 1e5 + 1, LIM = 62;
const int P[LIM] = {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};
const int ref[M] = {
    0, 0,  0,  1, 0,  2,  0, 3, 0,  0, 0,  4,  0, 5,  0, 0, 0,  6,  0, 7,  0,
    0, 0,  8,  0, 0,  0,  0, 0, 9,  0, 10, 0,  0, 0,  0, 0, 11, 0,  0, 0,  12,
    0, 13, 0,  0, 0,  14, 0, 0, 0,  0, 0,  15, 0, 0,  0, 0, 0,  16, 0, 17, 0,
    0, 0,  0,  0, 18, 0,  0, 0, 19, 0, 20, 0,  0, 0,  0, 0, 21, 0,  0, 0,  22,
    0, 0,  0,  0, 0,  23, 0, 0, 0,  0, 0,  0,  0, 24, 0, 0, 0,  25, 0, 26, 0,
    0, 0,  27, 0, 28, 0,  0, 0, 29, 0, 0,  0,  0, 0,  0, 0, 0,  0,  0, 0,  0,
    0, 30, 0,  0, 0,  31, 0, 0, 0,  0, 0,  32, 0, 33, 0, 0, 0,  0,  0, 0,  0,
    0, 0,  34, 0, 35, 0,  0, 0, 0,  0, 36, 0,  0, 0,  0, 0, 37, 0,  0, 0,  38,
    0, 0,  0,  0, 0,  39, 0, 0, 0,  0, 0,  40, 0, 41, 0, 0, 0,  0,  0, 0,  0,
    0, 0,  42, 0, 43, 0,  0, 0, 44, 0, 45, 0,  0, 0,  0, 0, 0,  0,  0, 0,  0,
    0, 46, 0,  0, 0,  0,  0, 0, 0,  0, 0,  0,  0, 47, 0, 0, 0,  48, 0, 49, 0,
    0, 0,  50, 0, 0,  0,  0, 0, 51, 0, 52, 0,  0, 0,  0, 0, 0,  0,  0, 0,  53,
    0, 0,  0,  0, 0,  54, 0, 0, 0,  0, 0,  55, 0, 0,  0, 0, 0,  56, 0, 57, 0,
    0, 0,  0,  0, 58, 0,  0, 0, 59, 0, 60, 0,  0, 0,  0, 0, 0,  0,  0, 0,  61};
inline int read();
struct Segment_Tree {
  int val[N << 2], tag[N << 2];
  long long now, Ans, f[N << 2], tagf[N << 2];
  inline int FP(int x, int k) {
    int t = 1;
    for (; k; k >>= 1, x = 1ll * x * x % 1000000007)
      if (k & 1) t = 1ll * t * x % 1000000007;
    return t;
  }
  void Build(int l, int r, int rt) {
    tag[rt] = 1;
    if (l == r) {
      int v = read();
      val[rt] = v;
      for (int i = 0; i < LIM && P[i] * P[i] <= v; ++i)
        if (!(v % P[i])) {
          f[rt] |= 1ll << i, v /= P[i];
          while (!(v % P[i])) v /= P[i];
        }
      if (v != 1) f[rt] |= 1ll << ref[v];
      return;
    }
    int m = l + r >> 1;
    Build(l, m, rt << 1), Build(m + 1, r, rt << 1 | 1),
        f[rt] = f[rt << 1] | f[rt << 1 | 1],
        val[rt] = 1ll * val[rt << 1] * val[rt << 1 | 1] % 1000000007;
  }
  inline void PushDown(int rt, int m) {
    int l = rt << 1, r = rt << 1 | 1;
    val[l] = 1ll * val[l] * FP(tag[rt], m - (m >> 1)) % 1000000007,
    tag[l] = 1ll * tag[l] * tag[rt] % 1000000007, f[l] |= tagf[rt],
    tagf[l] |= tagf[rt],
    val[r] = 1ll * val[r] * FP(tag[rt], m >> 1) % 1000000007,
    tag[r] = 1ll * tag[r] * tag[rt] % 1000000007, f[r] |= tagf[rt],
    tagf[r] |= tagf[rt], tag[rt] = 1, tagf[rt] = 0;
  }
  void Modify(int l, int r, int rt, int L, int R, int v) {
    if (L <= l && r <= R) {
      val[rt] = 1ll * val[rt] * FP(v, r - l + 1) % 1000000007,
      tag[rt] = 1ll * tag[rt] * v % 1000000007, f[rt] |= now, tagf[rt] |= now;
      return;
    }
    if (tag[rt] != 1) PushDown(rt, r - l + 1);
    int m = l + r >> 1;
    if (L <= m) Modify(l, m, rt << 1, L, R, v);
    if (m < R) Modify(m + 1, r, rt << 1 | 1, L, R, v);
    f[rt] = f[rt << 1] | f[rt << 1 | 1],
    val[rt] = 1ll * val[rt << 1] * val[rt << 1 | 1] % 1000000007;
  }
  int Query(int l, int r, int rt, int L, int R) {
    if (L <= l && r <= R) return Ans |= f[rt], val[rt];
    if (tag[rt] != 1) PushDown(rt, r - l + 1);
    int m = l + r >> 1;
    if (L <= m)
      if (m < R)
        return 1ll * Query(l, m, rt << 1, L, R) *
               Query(m + 1, r, rt << 1 | 1, L, R) % 1000000007;
      else
        return Query(l, m, rt << 1, L, R);
    return Query(m + 1, r, rt << 1 | 1, L, R);
  }
} T;
inline int read() {
  int now = 0;
  register char c = getchar();
  for (; !isdigit(c); c = getchar())
    ;
  for (; isdigit(c); now = now * 10 + c - 48, c = getchar())
    ;
  return now;
}
inline char GetOpt() {
  register char c;
  while (!isalpha(c = getchar()))
    ;
  return c;
}
int main() {
  static int inv[N], coef[N];
  inv[1] = 1;
  for (int i = 2; i < M; ++i)
    inv[i] =
        1ll * (1000000007 - 1000000007 / i) * inv[1000000007 % i] % 1000000007;
  for (int i = 0; i < LIM; ++i)
    coef[i] = 1ll * (P[i] - 1) * inv[P[i]] % 1000000007;
  int n = read(), q = read();
  T.Build(1, n, 1);
  while (q--) {
    if (GetOpt() == 'T') {
      T.Ans = 0;
      int l = read(), r = read(), val = T.Query(1, n, 1, l, r);
      for (int i = 0; i < LIM; ++i)
        if (T.Ans >> i & 1) val = 1ll * val * coef[i] % 1000000007;
      printf("%d\n", val);
    } else {
      int l = read(), r = read(), x = read(), v = x;
      long long now = 0;
      for (int i = 0; i < LIM && P[i] * P[i] <= v; ++i)
        if (!(v % P[i])) {
          now |= 1ll << i, v /= P[i];
          while (!(v % P[i])) v /= P[i];
        }
      if (v != 1) now |= 1ll << ref[v];
      T.now = now, T.Modify(1, n, 1, l, r, x);
    }
  }
  return 0;
}

### Prompt

Your task is to create a cpp solution to 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>
const int N = 4e5 + 5, M = 301, M2 = 1e5 + 1, LIM = 62;
const int P[LIM] = {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};
const int ref[M] = {
    0, 0,  0,  1, 0,  2,  0, 3, 0,  0, 0,  4,  0, 5,  0, 0, 0,  6,  0, 7,  0,
    0, 0,  8,  0, 0,  0,  0, 0, 9,  0, 10, 0,  0, 0,  0, 0, 11, 0,  0, 0,  12,
    0, 13, 0,  0, 0,  14, 0, 0, 0,  0, 0,  15, 0, 0,  0, 0, 0,  16, 0, 17, 0,
    0, 0,  0,  0, 18, 0,  0, 0, 19, 0, 20, 0,  0, 0,  0, 0, 21, 0,  0, 0,  22,
    0, 0,  0,  0, 0,  23, 0, 0, 0,  0, 0,  0,  0, 24, 0, 0, 0,  25, 0, 26, 0,
    0, 0,  27, 0, 28, 0,  0, 0, 29, 0, 0,  0,  0, 0,  0, 0, 0,  0,  0, 0,  0,
    0, 30, 0,  0, 0,  31, 0, 0, 0,  0, 0,  32, 0, 33, 0, 0, 0,  0,  0, 0,  0,
    0, 0,  34, 0, 35, 0,  0, 0, 0,  0, 36, 0,  0, 0,  0, 0, 37, 0,  0, 0,  38,
    0, 0,  0,  0, 0,  39, 0, 0, 0,  0, 0,  40, 0, 41, 0, 0, 0,  0,  0, 0,  0,
    0, 0,  42, 0, 43, 0,  0, 0, 44, 0, 45, 0,  0, 0,  0, 0, 0,  0,  0, 0,  0,
    0, 46, 0,  0, 0,  0,  0, 0, 0,  0, 0,  0,  0, 47, 0, 0, 0,  48, 0, 49, 0,
    0, 0,  50, 0, 0,  0,  0, 0, 51, 0, 52, 0,  0, 0,  0, 0, 0,  0,  0, 0,  53,
    0, 0,  0,  0, 0,  54, 0, 0, 0,  0, 0,  55, 0, 0,  0, 0, 0,  56, 0, 57, 0,
    0, 0,  0,  0, 58, 0,  0, 0, 59, 0, 60, 0,  0, 0,  0, 0, 0,  0,  0, 0,  61};
inline int read();
struct Segment_Tree {
  int val[N << 2], tag[N << 2];
  long long now, Ans, f[N << 2], tagf[N << 2];
  inline int FP(int x, int k) {
    int t = 1;
    for (; k; k >>= 1, x = 1ll * x * x % 1000000007)
      if (k & 1) t = 1ll * t * x % 1000000007;
    return t;
  }
  void Build(int l, int r, int rt) {
    tag[rt] = 1;
    if (l == r) {
      int v = read();
      val[rt] = v;
      for (int i = 0; i < LIM && P[i] * P[i] <= v; ++i)
        if (!(v % P[i])) {
          f[rt] |= 1ll << i, v /= P[i];
          while (!(v % P[i])) v /= P[i];
        }
      if (v != 1) f[rt] |= 1ll << ref[v];
      return;
    }
    int m = l + r >> 1;
    Build(l, m, rt << 1), Build(m + 1, r, rt << 1 | 1),
        f[rt] = f[rt << 1] | f[rt << 1 | 1],
        val[rt] = 1ll * val[rt << 1] * val[rt << 1 | 1] % 1000000007;
  }
  inline void PushDown(int rt, int m) {
    int l = rt << 1, r = rt << 1 | 1;
    val[l] = 1ll * val[l] * FP(tag[rt], m - (m >> 1)) % 1000000007,
    tag[l] = 1ll * tag[l] * tag[rt] % 1000000007, f[l] |= tagf[rt],
    tagf[l] |= tagf[rt],
    val[r] = 1ll * val[r] * FP(tag[rt], m >> 1) % 1000000007,
    tag[r] = 1ll * tag[r] * tag[rt] % 1000000007, f[r] |= tagf[rt],
    tagf[r] |= tagf[rt], tag[rt] = 1, tagf[rt] = 0;
  }
  void Modify(int l, int r, int rt, int L, int R, int v) {
    if (L <= l && r <= R) {
      val[rt] = 1ll * val[rt] * FP(v, r - l + 1) % 1000000007,
      tag[rt] = 1ll * tag[rt] * v % 1000000007, f[rt] |= now, tagf[rt] |= now;
      return;
    }
    if (tag[rt] != 1) PushDown(rt, r - l + 1);
    int m = l + r >> 1;
    if (L <= m) Modify(l, m, rt << 1, L, R, v);
    if (m < R) Modify(m + 1, r, rt << 1 | 1, L, R, v);
    f[rt] = f[rt << 1] | f[rt << 1 | 1],
    val[rt] = 1ll * val[rt << 1] * val[rt << 1 | 1] % 1000000007;
  }
  int Query(int l, int r, int rt, int L, int R) {
    if (L <= l && r <= R) return Ans |= f[rt], val[rt];
    if (tag[rt] != 1) PushDown(rt, r - l + 1);
    int m = l + r >> 1;
    if (L <= m)
      if (m < R)
        return 1ll * Query(l, m, rt << 1, L, R) *
               Query(m + 1, r, rt << 1 | 1, L, R) % 1000000007;
      else
        return Query(l, m, rt << 1, L, R);
    return Query(m + 1, r, rt << 1 | 1, L, R);
  }
} T;
inline int read() {
  int now = 0;
  register char c = getchar();
  for (; !isdigit(c); c = getchar())
    ;
  for (; isdigit(c); now = now * 10 + c - 48, c = getchar())
    ;
  return now;
}
inline char GetOpt() {
  register char c;
  while (!isalpha(c = getchar()))
    ;
  return c;
}
int main() {
  static int inv[N], coef[N];
  inv[1] = 1;
  for (int i = 2; i < M; ++i)
    inv[i] =
        1ll * (1000000007 - 1000000007 / i) * inv[1000000007 % i] % 1000000007;
  for (int i = 0; i < LIM; ++i)
    coef[i] = 1ll * (P[i] - 1) * inv[P[i]] % 1000000007;
  int n = read(), q = read();
  T.Build(1, n, 1);
  while (q--) {
    if (GetOpt() == 'T') {
      T.Ans = 0;
      int l = read(), r = read(), val = T.Query(1, n, 1, l, r);
      for (int i = 0; i < LIM; ++i)
        if (T.Ans >> i & 1) val = 1ll * val * coef[i] % 1000000007;
      printf("%d\n", val);
    } else {
      int l = read(), r = read(), x = read(), v = x;
      long long now = 0;
      for (int i = 0; i < LIM && P[i] * P[i] <= v; ++i)
        if (!(v % P[i])) {
          now |= 1ll << i, v /= P[i];
          while (!(v % P[i])) v /= P[i];
        }
      if (v != 1) now |= 1ll << ref[v];
      T.now = now, T.Modify(1, n, 1, l, r, x);
    }
  }
  return 0;
}

```