#include <bits/stdc++.h>
inline int getint() {
  register char ch;
  while (!isdigit(ch = getchar()))
    ;
  register int x = ch ^ '0';
  while (isdigit(ch = getchar())) x = (((x << 2) + x) << 1) + (ch ^ '0');
  return x;
}
inline char getalpha() {
  register char ch;
  while (!isalpha(ch = getchar()))
    ;
  return ch;
}
const int N = 4e5 + 1, Q = 2e5, A = 301, P = 63, mod = 1e9 + 7;
bool vis[A];
int p[P], pinv[P];
inline void sieve() {
  for (register int i = 2; i < A; i++) {
    if (!vis[i]) p[++p[0]] = i;
    for (register int j = 1; j <= p[0] && p[j] * i < A; j++) {
      vis[p[j] * i] = true;
      if (i % p[j] == 0) break;
    }
  }
}
void exgcd(const int &a, const int &b, int &x, int &y) {
  if (!b) {
    x = 1, y = 0;
    return;
  }
  exgcd(b, a % b, y, x);
  y -= a / b * x;
}
inline int inv(const int &x) {
  int ret, tmp;
  exgcd(x, mod, ret, tmp);
  return (ret % mod + mod) % mod;
}
inline void init() {
  sieve();
  for (register int i = 1; i < P; i++) {
    pinv[i] = inv(p[i]);
  }
}
inline long long get_bitmask(const int &x) {
  long long ret = 0;
  for (register int i = 1; i < P; i++) {
    if (x % p[i] == 0) ret |= 1ll << i;
  }
  return ret;
}
inline int calc(const long long &s) {
  int ret = 1;
  for (register int i = 1; i < P; i++) {
    if (s >> i & 1) {
      ret = 1ll * ret * (mod + 1 - pinv[i]) % mod;
    }
  }
  return ret;
}
inline int power(int a, int k) {
  int ret = 1;
  for (; k; k >>= 1) {
    if (k & 1) ret = 1ll * ret * a % mod;
    a = 1ll * a * a % mod;
  }
  return ret;
}
class SegmentTree1 {
 private:
  long long val[N << 2], tag[N << 2];
  void push_down(const int &p) {
    if (!tag[p]) return;
    tag[p << 1] |= tag[p];
    tag[p << 1 | 1] |= tag[p];
    val[p << 1] |= tag[p];
    val[p << 1 | 1] |= tag[p];
    tag[p] = 0;
  }

 public:
  void modify(const int &p, const int &b, const int &e, const int &l,
              const int &r, const long long &x) {
    val[p] |= x;
    if (b == l && e == r) {
      tag[p] |= x;
      return;
    }
    push_down(p);
    if (l <= ((b + e) >> 1))
      modify(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r), x);
    if (r > ((b + e) >> 1))
      modify(p << 1 | 1, ((b + e) >> 1) + 1, e, std::max(((b + e) >> 1) + 1, l),
             r, x);
  }
  long long query(const int &p, const int &b, const int &e, const int &l,
                  const int &r) {
    if (b == l && e == r) return val[p];
    long long ret = 0;
    push_down(p);
    if (l <= ((b + e) >> 1))
      ret |= query(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r));
    if (r > ((b + e) >> 1))
      ret |= query(p << 1 | 1, ((b + e) >> 1) + 1, e,
                   std::max(((b + e) >> 1) + 1, l), r);
    return ret;
  }
};
SegmentTree1 t1;
class SegmentTree2 {
 private:
  int val[N << 2], tag[N << 2];
  int len(const int &b, const int &e) const { return e - b + 1; }
  void push_down(const int &p, const int &b, const int &e) {
    if (tag[p] == 1) return;
    tag[p << 1] = 1ll * tag[p << 1] * tag[p] % mod;
    tag[p << 1 | 1] = 1ll * tag[p << 1 | 1] * tag[p] % mod;
    val[p << 1] =
        1ll * val[p << 1] * power(tag[p], len(b, ((b + e) >> 1))) % mod;
    val[p << 1 | 1] =
        1ll * val[p << 1 | 1] * power(tag[p], len(((b + e) >> 1) + 1, e)) % mod;
    tag[p] = 1;
  }
  void push_up(const int &p) {
    val[p] = 1ll * val[p << 1] * val[p << 1 | 1] % mod;
  }

 public:
  void build(const int &p, const int &b, const int &e) {
    val[p] = tag[p] = 1;
    if (b == e) return;
    build(p << 1, b, ((b + e) >> 1));
    build(p << 1 | 1, ((b + e) >> 1) + 1, e);
  }
  void modify(const int &p, const int &b, const int &e, const int &l,
              const int &r, const int &x) {
    if (b == l && e == r) {
      val[p] = 1ll * val[p] * power(x, len(b, e)) % mod;
      tag[p] = 1ll * tag[p] * x % mod;
      return;
    }
    push_down(p, b, e);
    if (l <= ((b + e) >> 1))
      modify(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r), x);
    if (r > ((b + e) >> 1))
      modify(p << 1 | 1, ((b + e) >> 1) + 1, e, std::max(((b + e) >> 1) + 1, l),
             r, x);
    push_up(p);
  }
  int query(const int &p, const int &b, const int &e, const int &l,
            const int &r) {
    if (b == l && e == r) return val[p];
    int ret = 1;
    push_down(p, b, e);
    if (l <= ((b + e) >> 1))
      ret = 1ll * ret *
            query(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r)) %
            mod;
    if (r > ((b + e) >> 1))
      ret = 1ll * ret *
            query(p << 1 | 1, ((b + e) >> 1) + 1, e,
                  std::max(((b + e) >> 1) + 1, l), r) %
            mod;
    return ret;
  }
};
SegmentTree2 t2;
int main() {
  init();
  const int n = getint(), m = getint();
  t2.build(1, 1, n);
  for (register int i = 1; i <= n; i++) {
    const int a = getint();
    t1.modify(1, 1, n, i, i, get_bitmask(a));
    t2.modify(1, 1, n, i, i, a);
  }
  for (register int i = 0; i < m; i++) {
    const char ch = getalpha();
    const int l = getint(), r = getint();
    if (ch == 'M') {
      const int x = getint();
      t1.modify(1, 1, n, l, r, get_bitmask(x));
      t2.modify(1, 1, n, l, r, x);
    }
    if (ch == 'T') {
      printf("%lld\n", 1ll * calc(t1.query(1, 1, n, l, r)) *
                           t2.query(1, 1, n, l, r) % mod);
    }
  }
  return 0;
}

### Prompt

Create a solution in cpp for 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>
inline int getint() {
  register char ch;
  while (!isdigit(ch = getchar()))
    ;
  register int x = ch ^ '0';
  while (isdigit(ch = getchar())) x = (((x << 2) + x) << 1) + (ch ^ '0');
  return x;
}
inline char getalpha() {
  register char ch;
  while (!isalpha(ch = getchar()))
    ;
  return ch;
}
const int N = 4e5 + 1, Q = 2e5, A = 301, P = 63, mod = 1e9 + 7;
bool vis[A];
int p[P], pinv[P];
inline void sieve() {
  for (register int i = 2; i < A; i++) {
    if (!vis[i]) p[++p[0]] = i;
    for (register int j = 1; j <= p[0] && p[j] * i < A; j++) {
      vis[p[j] * i] = true;
      if (i % p[j] == 0) break;
    }
  }
}
void exgcd(const int &a, const int &b, int &x, int &y) {
  if (!b) {
    x = 1, y = 0;
    return;
  }
  exgcd(b, a % b, y, x);
  y -= a / b * x;
}
inline int inv(const int &x) {
  int ret, tmp;
  exgcd(x, mod, ret, tmp);
  return (ret % mod + mod) % mod;
}
inline void init() {
  sieve();
  for (register int i = 1; i < P; i++) {
    pinv[i] = inv(p[i]);
  }
}
inline long long get_bitmask(const int &x) {
  long long ret = 0;
  for (register int i = 1; i < P; i++) {
    if (x % p[i] == 0) ret |= 1ll << i;
  }
  return ret;
}
inline int calc(const long long &s) {
  int ret = 1;
  for (register int i = 1; i < P; i++) {
    if (s >> i & 1) {
      ret = 1ll * ret * (mod + 1 - pinv[i]) % mod;
    }
  }
  return ret;
}
inline int power(int a, int k) {
  int ret = 1;
  for (; k; k >>= 1) {
    if (k & 1) ret = 1ll * ret * a % mod;
    a = 1ll * a * a % mod;
  }
  return ret;
}
class SegmentTree1 {
 private:
  long long val[N << 2], tag[N << 2];
  void push_down(const int &p) {
    if (!tag[p]) return;
    tag[p << 1] |= tag[p];
    tag[p << 1 | 1] |= tag[p];
    val[p << 1] |= tag[p];
    val[p << 1 | 1] |= tag[p];
    tag[p] = 0;
  }

 public:
  void modify(const int &p, const int &b, const int &e, const int &l,
              const int &r, const long long &x) {
    val[p] |= x;
    if (b == l && e == r) {
      tag[p] |= x;
      return;
    }
    push_down(p);
    if (l <= ((b + e) >> 1))
      modify(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r), x);
    if (r > ((b + e) >> 1))
      modify(p << 1 | 1, ((b + e) >> 1) + 1, e, std::max(((b + e) >> 1) + 1, l),
             r, x);
  }
  long long query(const int &p, const int &b, const int &e, const int &l,
                  const int &r) {
    if (b == l && e == r) return val[p];
    long long ret = 0;
    push_down(p);
    if (l <= ((b + e) >> 1))
      ret |= query(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r));
    if (r > ((b + e) >> 1))
      ret |= query(p << 1 | 1, ((b + e) >> 1) + 1, e,
                   std::max(((b + e) >> 1) + 1, l), r);
    return ret;
  }
};
SegmentTree1 t1;
class SegmentTree2 {
 private:
  int val[N << 2], tag[N << 2];
  int len(const int &b, const int &e) const { return e - b + 1; }
  void push_down(const int &p, const int &b, const int &e) {
    if (tag[p] == 1) return;
    tag[p << 1] = 1ll * tag[p << 1] * tag[p] % mod;
    tag[p << 1 | 1] = 1ll * tag[p << 1 | 1] * tag[p] % mod;
    val[p << 1] =
        1ll * val[p << 1] * power(tag[p], len(b, ((b + e) >> 1))) % mod;
    val[p << 1 | 1] =
        1ll * val[p << 1 | 1] * power(tag[p], len(((b + e) >> 1) + 1, e)) % mod;
    tag[p] = 1;
  }
  void push_up(const int &p) {
    val[p] = 1ll * val[p << 1] * val[p << 1 | 1] % mod;
  }

 public:
  void build(const int &p, const int &b, const int &e) {
    val[p] = tag[p] = 1;
    if (b == e) return;
    build(p << 1, b, ((b + e) >> 1));
    build(p << 1 | 1, ((b + e) >> 1) + 1, e);
  }
  void modify(const int &p, const int &b, const int &e, const int &l,
              const int &r, const int &x) {
    if (b == l && e == r) {
      val[p] = 1ll * val[p] * power(x, len(b, e)) % mod;
      tag[p] = 1ll * tag[p] * x % mod;
      return;
    }
    push_down(p, b, e);
    if (l <= ((b + e) >> 1))
      modify(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r), x);
    if (r > ((b + e) >> 1))
      modify(p << 1 | 1, ((b + e) >> 1) + 1, e, std::max(((b + e) >> 1) + 1, l),
             r, x);
    push_up(p);
  }
  int query(const int &p, const int &b, const int &e, const int &l,
            const int &r) {
    if (b == l && e == r) return val[p];
    int ret = 1;
    push_down(p, b, e);
    if (l <= ((b + e) >> 1))
      ret = 1ll * ret *
            query(p << 1, b, ((b + e) >> 1), l, std::min(((b + e) >> 1), r)) %
            mod;
    if (r > ((b + e) >> 1))
      ret = 1ll * ret *
            query(p << 1 | 1, ((b + e) >> 1) + 1, e,
                  std::max(((b + e) >> 1) + 1, l), r) %
            mod;
    return ret;
  }
};
SegmentTree2 t2;
int main() {
  init();
  const int n = getint(), m = getint();
  t2.build(1, 1, n);
  for (register int i = 1; i <= n; i++) {
    const int a = getint();
    t1.modify(1, 1, n, i, i, get_bitmask(a));
    t2.modify(1, 1, n, i, i, a);
  }
  for (register int i = 0; i < m; i++) {
    const char ch = getalpha();
    const int l = getint(), r = getint();
    if (ch == 'M') {
      const int x = getint();
      t1.modify(1, 1, n, l, r, get_bitmask(x));
      t2.modify(1, 1, n, l, r, x);
    }
    if (ch == 'T') {
      printf("%lld\n", 1ll * calc(t1.query(1, 1, n, l, r)) *
                           t2.query(1, 1, n, l, r) % mod);
    }
  }
  return 0;
}

```