#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
using LL = long long;
const LL MOD = 1e9 + 7;
LL modpow(LL a, LL n) {
  if (n < 0) {
    a = modpow(a, MOD - 2);
    n = -n;
  }
  LL res = 1;
  for (a %= MOD; n > 0; n >>= 1) {
    if (n & 1) res = (res * a) % MOD;
    a = (a * a) % MOD;
  }
  return res;
}
const int N = 4e5, M = 301, P = 62;
LL prime_mask[M];
class SegmentTree {
  vector<LL> tree, lazy;
  vector<LL> mtree, mlazy;
  int sz;
  void split(int node, int x, int y) {
    if (lazy[node] != 1) {
      int z = (x + y) / 2;
      LL val = modpow(lazy[node], min(z - x, y - z));
      LL val1 = val, val2 = val;
      if (z - x > y - z) val1 = (val1 * lazy[node]) % MOD;
      if (z - x < y - z) val2 = (val2 * lazy[node]) % MOD;
      tree[2 * node] = (tree[2 * node] * val1) % MOD;
      lazy[2 * node] = (lazy[2 * node] * lazy[node]) % MOD;
      tree[2 * node + 1] = (tree[2 * node + 1] * val2) % MOD;
      lazy[2 * node + 1] = (lazy[2 * node + 1] * lazy[node]) % MOD;
      lazy[node] = 1;
    }
    mtree[2 * node] |= mlazy[node];
    mlazy[2 * node] |= mlazy[node];
    mtree[2 * node + 1] |= mlazy[node];
    mlazy[2 * node + 1] |= mlazy[node];
  }
  void merge(int node, int x, int y) {
    tree[node] = (tree[2 * node] * tree[2 * node + 1]) % MOD;
    mtree[node] = mtree[2 * node] | mtree[2 * node + 1];
  }

 public:
  SegmentTree(int n) {
    for (sz = 1; sz < n; sz <<= 1)
      ;
    tree.resize(2 * sz, 1);
    lazy.resize(2 * sz, 1);
    mtree.resize(2 * sz, 0);
    mlazy.resize(2 * sz, 0);
  }
  void update(int l, int r, int d, int node = 1, int x = 0, int y = -1) {
    if (y == -1) y = sz;
    if (l >= y || r <= x) return;
    if (l <= x && r >= y) {
      tree[node] = (tree[node] * modpow(d, y - x)) % MOD;
      lazy[node] = (lazy[node] * d) % MOD;
      mtree[node] |= prime_mask[d];
      mlazy[node] |= prime_mask[d];
      return;
    }
    split(node, x, y);
    update(l, r, d, 2 * node, x, (x + y) / 2);
    update(l, r, d, 2 * node + 1, (x + y) / 2, y);
    merge(node, x, y);
  }
  pair<LL, LL> query(int l, int r, int node = 1, int x = 0, int y = -1) {
    if (y == -1) y = sz;
    if (l >= y || r <= x) return {1, 0};
    if (l <= x && r >= y) {
      return {tree[node], mtree[node]};
    }
    split(node, x, y);
    auto lres = query(l, r, 2 * node, x, (x + y) / 2);
    auto rres = query(l, r, 2 * node + 1, (x + y) / 2, y);
    merge(node, x, y);
    return {(lres.first * rres.first) % MOD, lres.second | rres.second};
  }
};
LL mult[P];
void prec() {
  map<int, int> pid;
  vector<bool> isprime(M, true);
  for (int i = 2; i < M; i++) {
    if (isprime[i]) {
      int idx = pid.size();
      pid[i] = idx;
      mult[idx] = ((i - 1) * modpow(i, -1)) % MOD;
      for (int j = 2 * i; j < M; j += i) isprime[j] = false;
    }
    for (int val = i, p = 2; val > 1 && p <= val; p++) {
      while (val % p == 0) val /= p, prime_mask[i] |= 1ll << pid[p];
    }
  }
}
LL get_phi(LL mask) {
  LL res = 1;
  for (int i = 0; i < 62; i++) {
    if ((mask >> i) & 1) {
      res = (res * mult[i]) % MOD;
    }
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  prec();
  int n, q;
  cin >> n >> q;
  SegmentTree st(n);
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    st.update(i, i + 1, a);
  }
  while (q--) {
    string ty;
    int l, r;
    cin >> ty >> l >> r;
    if (ty[0] == 'M') {
      int a;
      cin >> a;
      st.update(l - 1, r, a);
    } else {
      auto res = st.query(l - 1, r);
      LL ans = (res.first * get_phi(res.second)) % MOD;
      cout << ans << '\n';
    }
  }
  return 0;
}

### Prompt

Your challenge is to write 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>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
using LL = long long;
const LL MOD = 1e9 + 7;
LL modpow(LL a, LL n) {
  if (n < 0) {
    a = modpow(a, MOD - 2);
    n = -n;
  }
  LL res = 1;
  for (a %= MOD; n > 0; n >>= 1) {
    if (n & 1) res = (res * a) % MOD;
    a = (a * a) % MOD;
  }
  return res;
}
const int N = 4e5, M = 301, P = 62;
LL prime_mask[M];
class SegmentTree {
  vector<LL> tree, lazy;
  vector<LL> mtree, mlazy;
  int sz;
  void split(int node, int x, int y) {
    if (lazy[node] != 1) {
      int z = (x + y) / 2;
      LL val = modpow(lazy[node], min(z - x, y - z));
      LL val1 = val, val2 = val;
      if (z - x > y - z) val1 = (val1 * lazy[node]) % MOD;
      if (z - x < y - z) val2 = (val2 * lazy[node]) % MOD;
      tree[2 * node] = (tree[2 * node] * val1) % MOD;
      lazy[2 * node] = (lazy[2 * node] * lazy[node]) % MOD;
      tree[2 * node + 1] = (tree[2 * node + 1] * val2) % MOD;
      lazy[2 * node + 1] = (lazy[2 * node + 1] * lazy[node]) % MOD;
      lazy[node] = 1;
    }
    mtree[2 * node] |= mlazy[node];
    mlazy[2 * node] |= mlazy[node];
    mtree[2 * node + 1] |= mlazy[node];
    mlazy[2 * node + 1] |= mlazy[node];
  }
  void merge(int node, int x, int y) {
    tree[node] = (tree[2 * node] * tree[2 * node + 1]) % MOD;
    mtree[node] = mtree[2 * node] | mtree[2 * node + 1];
  }

 public:
  SegmentTree(int n) {
    for (sz = 1; sz < n; sz <<= 1)
      ;
    tree.resize(2 * sz, 1);
    lazy.resize(2 * sz, 1);
    mtree.resize(2 * sz, 0);
    mlazy.resize(2 * sz, 0);
  }
  void update(int l, int r, int d, int node = 1, int x = 0, int y = -1) {
    if (y == -1) y = sz;
    if (l >= y || r <= x) return;
    if (l <= x && r >= y) {
      tree[node] = (tree[node] * modpow(d, y - x)) % MOD;
      lazy[node] = (lazy[node] * d) % MOD;
      mtree[node] |= prime_mask[d];
      mlazy[node] |= prime_mask[d];
      return;
    }
    split(node, x, y);
    update(l, r, d, 2 * node, x, (x + y) / 2);
    update(l, r, d, 2 * node + 1, (x + y) / 2, y);
    merge(node, x, y);
  }
  pair<LL, LL> query(int l, int r, int node = 1, int x = 0, int y = -1) {
    if (y == -1) y = sz;
    if (l >= y || r <= x) return {1, 0};
    if (l <= x && r >= y) {
      return {tree[node], mtree[node]};
    }
    split(node, x, y);
    auto lres = query(l, r, 2 * node, x, (x + y) / 2);
    auto rres = query(l, r, 2 * node + 1, (x + y) / 2, y);
    merge(node, x, y);
    return {(lres.first * rres.first) % MOD, lres.second | rres.second};
  }
};
LL mult[P];
void prec() {
  map<int, int> pid;
  vector<bool> isprime(M, true);
  for (int i = 2; i < M; i++) {
    if (isprime[i]) {
      int idx = pid.size();
      pid[i] = idx;
      mult[idx] = ((i - 1) * modpow(i, -1)) % MOD;
      for (int j = 2 * i; j < M; j += i) isprime[j] = false;
    }
    for (int val = i, p = 2; val > 1 && p <= val; p++) {
      while (val % p == 0) val /= p, prime_mask[i] |= 1ll << pid[p];
    }
  }
}
LL get_phi(LL mask) {
  LL res = 1;
  for (int i = 0; i < 62; i++) {
    if ((mask >> i) & 1) {
      res = (res * mult[i]) % MOD;
    }
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  prec();
  int n, q;
  cin >> n >> q;
  SegmentTree st(n);
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    st.update(i, i + 1, a);
  }
  while (q--) {
    string ty;
    int l, r;
    cin >> ty >> l >> r;
    if (ty[0] == 'M') {
      int a;
      cin >> a;
      st.update(l - 1, r, a);
    } else {
      auto res = st.query(l - 1, r);
      LL ans = (res.first * get_phi(res.second)) % MOD;
      cout << ans << '\n';
    }
  }
  return 0;
}

```