#include <bits/stdc++.h>
using namespace std;
template <typename T>
inline void read(T &s) {
  s = 0;
  char ch = getchar();
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) s = ((s + (s << 2)) << 1) + ch - '0', ch = getchar();
}
int n, q, zhi[310], zl, Inv[310], a[410000];
bool used[310];
bitset<63> val[310];
struct Point {
  int tot, tmp;
  bitset<63> s, tmps;
} tr[410000 << 3];
inline int Fast_Power(int u, int k = 1000000007 - 2) {
  int Sum = 1;
  while (k) {
    if (k & 1) Sum = 1ll * Sum * u % 1000000007;
    u = (long long)u * u % 1000000007, k >>= 1;
  }
  return Sum;
}
inline void Get_val() {
  for (int i = 2; i <= 300; ++i) {
    if (!used[i]) zhi[++zl] = i, Inv[zl] = Fast_Power(i);
    for (int j = 1; j <= zl && zhi[j] * i <= 300; ++j) {
      used[zhi[j] * i] = 1;
      if (i % zhi[j] == 0) break;
    }
  }
  for (int i = 2; i <= 300; ++i)
    for (int j = 1; j <= zl; ++j)
      if (i % zhi[j] == 0) val[i].set(j - 1);
}
inline void Update(int now) {
  tr[now].tot = 1ll * tr[now << 1].tot * tr[now << 1 | 1].tot % 1000000007,
  tr[now].s = tr[now << 1].s | tr[now << 1 | 1].s;
}
inline void Pushdown(int now, int l, int r) {
  int mid = (l + r) >> 1;
  if (tr[now].tmp != 1) {
    tr[now << 1].tot = 1ll * tr[now << 1].tot *
                       Fast_Power(tr[now].tmp, mid - l + 1) % 1000000007,
              tr[now << 1 | 1].tot = 1ll * tr[now << 1 | 1].tot *
                                     Fast_Power(tr[now].tmp, r - mid) %
                                     1000000007;
    tr[now << 1].tmp = 1ll * tr[now << 1].tmp * tr[now].tmp % 1000000007,
              tr[now << 1 | 1].tmp =
                  1ll * tr[now << 1 | 1].tmp * tr[now].tmp % 1000000007;
    tr[now].tmp = 1;
  }
  if (tr[now].tmps != 0) {
    tr[now << 1].s |= tr[now].tmps,
        tr[now << 1 | 1].s = tr[now << 1 | 1].s | tr[now].tmps;
    tr[now << 1].tmps |= tr[now].tmps, tr[now << 1 | 1].tmps |= tr[now].tmps;
    tr[now].tmps = 0;
  }
}
inline void Build(int now, int l, int r) {
  tr[now].s = tr[now].tmps = 0, tr[now].tot = tr[now].tmp = 1;
  if (l == r) return (void)(tr[now].tot = a[l], tr[now].s = val[a[l]]);
  int mid = (l + r) >> 1;
  Build(now << 1, l, mid), Build(now << 1 | 1, mid + 1, r), Update(now);
}
inline void Modify(int now, int l, int r, int ql, int qr, int x) {
  if (ql <= l && r <= qr) {
    tr[now].tot = 1ll * tr[now].tot * Fast_Power(x, r - l + 1) % 1000000007,
    tr[now].tmp = 1ll * tr[now].tmp * x % 1000000007;
    tr[now].s |= val[x], tr[now].tmps |= val[x];
    return;
  }
  Pushdown(now, l, r);
  int mid = (l + r) >> 1;
  if (mid < qr) Modify(now << 1 | 1, mid + 1, r, ql, qr, x);
  if (mid >= ql) Modify(now << 1, l, mid, ql, qr, x);
  Update(now);
}
inline int Querytot(int now, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return tr[now].tot;
  Pushdown(now, l, r);
  int mid = (l + r) >> 1, Sum = 1;
  if (mid < qr)
    Sum = 1ll * Sum * Querytot(now << 1 | 1, mid + 1, r, ql, qr) % 1000000007;
  if (mid >= ql)
    Sum = 1ll * Sum * Querytot(now << 1, l, mid, ql, qr) % 1000000007;
  return Sum;
}
inline bitset<63> Querys(int now, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return tr[now].s;
  Pushdown(now, l, r);
  int mid = (l + r) >> 1;
  bitset<63> Sum = 0;
  if (mid < qr) Sum |= Querys(now << 1 | 1, mid + 1, r, ql, qr);
  if (mid >= ql) Sum |= Querys(now << 1, l, mid, ql, qr);
  return Sum;
}
inline void Query(int l, int r) {
  int Sum = Querytot(1, 1, n, l, r);
  bitset<63> S = Querys(1, 1, n, l, r);
  for (int i = 0; i < zl; ++i)
    if (S.test(i))
      Sum = 1ll * Sum * Inv[i + 1] % 1000000007 * (zhi[i + 1] - 1) % 1000000007;
  printf("%d\n", Sum);
}
int main() {
  Get_val(), read(n), read(q);
  for (int i = 1; i <= n; ++i) read(a[i]);
  Build(1, 1, n);
  string s;
  int l, r, x;
  while (q--) {
    cin >> s;
    if (s == "MULTIPLY")
      read(l), read(r), read(x), Modify(1, 1, n, l, r, x);
    else
      read(l), read(r), Query(l, r);
  }
  return 0;
}

### Prompt

Generate 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>
using namespace std;
template <typename T>
inline void read(T &s) {
  s = 0;
  char ch = getchar();
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) s = ((s + (s << 2)) << 1) + ch - '0', ch = getchar();
}
int n, q, zhi[310], zl, Inv[310], a[410000];
bool used[310];
bitset<63> val[310];
struct Point {
  int tot, tmp;
  bitset<63> s, tmps;
} tr[410000 << 3];
inline int Fast_Power(int u, int k = 1000000007 - 2) {
  int Sum = 1;
  while (k) {
    if (k & 1) Sum = 1ll * Sum * u % 1000000007;
    u = (long long)u * u % 1000000007, k >>= 1;
  }
  return Sum;
}
inline void Get_val() {
  for (int i = 2; i <= 300; ++i) {
    if (!used[i]) zhi[++zl] = i, Inv[zl] = Fast_Power(i);
    for (int j = 1; j <= zl && zhi[j] * i <= 300; ++j) {
      used[zhi[j] * i] = 1;
      if (i % zhi[j] == 0) break;
    }
  }
  for (int i = 2; i <= 300; ++i)
    for (int j = 1; j <= zl; ++j)
      if (i % zhi[j] == 0) val[i].set(j - 1);
}
inline void Update(int now) {
  tr[now].tot = 1ll * tr[now << 1].tot * tr[now << 1 | 1].tot % 1000000007,
  tr[now].s = tr[now << 1].s | tr[now << 1 | 1].s;
}
inline void Pushdown(int now, int l, int r) {
  int mid = (l + r) >> 1;
  if (tr[now].tmp != 1) {
    tr[now << 1].tot = 1ll * tr[now << 1].tot *
                       Fast_Power(tr[now].tmp, mid - l + 1) % 1000000007,
              tr[now << 1 | 1].tot = 1ll * tr[now << 1 | 1].tot *
                                     Fast_Power(tr[now].tmp, r - mid) %
                                     1000000007;
    tr[now << 1].tmp = 1ll * tr[now << 1].tmp * tr[now].tmp % 1000000007,
              tr[now << 1 | 1].tmp =
                  1ll * tr[now << 1 | 1].tmp * tr[now].tmp % 1000000007;
    tr[now].tmp = 1;
  }
  if (tr[now].tmps != 0) {
    tr[now << 1].s |= tr[now].tmps,
        tr[now << 1 | 1].s = tr[now << 1 | 1].s | tr[now].tmps;
    tr[now << 1].tmps |= tr[now].tmps, tr[now << 1 | 1].tmps |= tr[now].tmps;
    tr[now].tmps = 0;
  }
}
inline void Build(int now, int l, int r) {
  tr[now].s = tr[now].tmps = 0, tr[now].tot = tr[now].tmp = 1;
  if (l == r) return (void)(tr[now].tot = a[l], tr[now].s = val[a[l]]);
  int mid = (l + r) >> 1;
  Build(now << 1, l, mid), Build(now << 1 | 1, mid + 1, r), Update(now);
}
inline void Modify(int now, int l, int r, int ql, int qr, int x) {
  if (ql <= l && r <= qr) {
    tr[now].tot = 1ll * tr[now].tot * Fast_Power(x, r - l + 1) % 1000000007,
    tr[now].tmp = 1ll * tr[now].tmp * x % 1000000007;
    tr[now].s |= val[x], tr[now].tmps |= val[x];
    return;
  }
  Pushdown(now, l, r);
  int mid = (l + r) >> 1;
  if (mid < qr) Modify(now << 1 | 1, mid + 1, r, ql, qr, x);
  if (mid >= ql) Modify(now << 1, l, mid, ql, qr, x);
  Update(now);
}
inline int Querytot(int now, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return tr[now].tot;
  Pushdown(now, l, r);
  int mid = (l + r) >> 1, Sum = 1;
  if (mid < qr)
    Sum = 1ll * Sum * Querytot(now << 1 | 1, mid + 1, r, ql, qr) % 1000000007;
  if (mid >= ql)
    Sum = 1ll * Sum * Querytot(now << 1, l, mid, ql, qr) % 1000000007;
  return Sum;
}
inline bitset<63> Querys(int now, int l, int r, int ql, int qr) {
  if (ql <= l && r <= qr) return tr[now].s;
  Pushdown(now, l, r);
  int mid = (l + r) >> 1;
  bitset<63> Sum = 0;
  if (mid < qr) Sum |= Querys(now << 1 | 1, mid + 1, r, ql, qr);
  if (mid >= ql) Sum |= Querys(now << 1, l, mid, ql, qr);
  return Sum;
}
inline void Query(int l, int r) {
  int Sum = Querytot(1, 1, n, l, r);
  bitset<63> S = Querys(1, 1, n, l, r);
  for (int i = 0; i < zl; ++i)
    if (S.test(i))
      Sum = 1ll * Sum * Inv[i + 1] % 1000000007 * (zhi[i + 1] - 1) % 1000000007;
  printf("%d\n", Sum);
}
int main() {
  Get_val(), read(n), read(q);
  for (int i = 1; i <= n; ++i) read(a[i]);
  Build(1, 1, n);
  string s;
  int l, r, x;
  while (q--) {
    cin >> s;
    if (s == "MULTIPLY")
      read(l), read(r), read(x), Modify(1, 1, n, l, r, x);
    else
      read(l), read(r), Query(l, r);
  }
  return 0;
}

```