#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const long long INFF = 0x3f3f3f3f3f3f3f3fll;
const long long M = 1e9 + 7;
const long long maxn = 4e5 + 107;
const double pi = acos(-1.0);
const double eps = 0.0000000001;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
template <typename T>
inline void pr2(T x, int k = 64) {
  long long i;
  for (i = 0; i < k; i++) fprintf(stderr, "%d", (x >> i) & 1);
  putchar(' ');
}
template <typename T>
inline void add_(T &A, int B, long long MOD = M) {
  A += B;
  (A >= MOD) && (A -= MOD);
}
template <typename T>
inline void mul_(T &A, long long B, long long MOD = M) {
  A = (A * B) % MOD;
}
template <typename T>
inline void mod_(T &A, long long MOD = M) {
  A %= MOD;
  A += MOD;
  A %= MOD;
}
template <typename T>
inline void max_(T &A, T B) {
  (A < B) && (A = B);
}
template <typename T>
inline void min_(T &A, T B) {
  (A > B) && (A = B);
}
template <typename T>
inline T abs(T a) {
  return a > 0 ? a : -a;
}
template <typename T>
inline T powMM(T a, T b) {
  T ret = 1;
  for (; b; b >>= 1ll, a = (long long)a * a % M)
    if (b & 1) ret = (long long)ret * a % M;
  return ret;
}
int startTime;
void startTimer() { startTime = clock(); }
void printTimer() {
  fprintf(stderr, "/--- Time: %ld milliseconds ---/\n", clock() - startTime);
}
int n, m, q;
int A[maxn];
long long val[maxn * 4], lazyval[maxn * 4], bit[307];
long long sum[maxn * 4], lazysum[maxn * 4];
void change(int x, int len, int mul, long long xo) {
  sum[x] = sum[x] * powMM(mul, len) % M;
  lazysum[x] = lazysum[x] * mul % M;
  val[x] = val[x] | xo;
  lazyval[x] |= xo;
}
void pushdown(int x, int L, int mid, int R) {
  if (lazyval[x]) {
    change(x << 1, mid - L + 1, lazysum[x], lazyval[x]);
    change(x << 1 | 1, R - mid, lazysum[x], lazyval[x]);
    lazysum[x] = 1;
    lazyval[x] = 0;
  }
}
void pushup(int x) {
  sum[x] = sum[x << 1] * sum[x << 1 | 1] % M;
  val[x] = val[x << 1] | val[x << 1 | 1];
}
void build(int x, int l, int r) {
  if (l == r) {
    val[x] = bit[A[l]];
    sum[x] = A[l];
    return;
  }
  int mid = (l + r) / 2;
  build(x << 1, l, mid);
  build(x << 1 | 1, mid + 1, r);
  pushup(x);
  lazysum[x] = 1;
}
void update(int x, int l, int r, int v, int L, int R) {
  if (l <= L && R <= r) {
    change(x, R - L + 1, v, bit[v]);
    return;
  }
  int mid = (L + R) / 2;
  pushdown(x, L, mid, R);
  if (l <= mid) update(x << 1, l, r, v, L, mid);
  if (mid < r) update(x << 1 | 1, l, r, v, mid + 1, R);
  pushup(x);
}
pair<long long, long long> merge(pair<long long, long long> A,
                                 pair<long long, long long> B) {
  return make_pair(A.first * B.first % M, A.second | B.second);
}
pair<long long, long long> query(int x, int l, int r, int L, int R) {
  if (l <= L && R <= r) return make_pair(sum[x], val[x]);
  int mid = (L + R) / 2;
  pair<long long, long long> ret = make_pair(1, 0);
  pushdown(x, L, mid, R);
  if (l <= mid) ret = merge(ret, query(x << 1, l, r, L, mid));
  if (mid < r) ret = merge(ret, query(x << 1 | 1, l, r, mid + 1, R));
  pushup(x);
  return ret;
}
int p[1007];
int chk[1007];
int main() {
  int i, j, C = 0;
  for (i = 2; i <= 300; i++)
    if (!bit[i]) {
      for (j = i; j <= 300; j += i) bit[j] |= 1ll << C;
      chk[C] = powMM((long long)i, M - 2) * (i - 1) % M;
      p[C++] = i;
    }
  scanf("%d%d", &n, &q);
  for (i = 1; i <= n; i++) scanf("%d", &A[i]);
  build(1, 1, n);
  while (q--) {
    char op[107];
    scanf("%s", op);
    if (op[0] == 'T') {
      int l, r;
      scanf("%d%d", &l, &r);
      pair<long long, long long> ans = query(1, l, r, 1, n);
      for (i = 0; i < 62; i++)
        if ((ans.second >> i) & 1) ans.first = ans.first * chk[i] % M;
      printf("%lld\n", ans.first);
    } else {
      int l, r, x;
      scanf("%d%d%d", &l, &r, &x);
      update(1, l, r, x, 1, n);
    }
  }
}

### Prompt

Please formulate 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;
const int INF = 0x3f3f3f3f;
const long long INFF = 0x3f3f3f3f3f3f3f3fll;
const long long M = 1e9 + 7;
const long long maxn = 4e5 + 107;
const double pi = acos(-1.0);
const double eps = 0.0000000001;
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
template <typename T>
inline void pr2(T x, int k = 64) {
  long long i;
  for (i = 0; i < k; i++) fprintf(stderr, "%d", (x >> i) & 1);
  putchar(' ');
}
template <typename T>
inline void add_(T &A, int B, long long MOD = M) {
  A += B;
  (A >= MOD) && (A -= MOD);
}
template <typename T>
inline void mul_(T &A, long long B, long long MOD = M) {
  A = (A * B) % MOD;
}
template <typename T>
inline void mod_(T &A, long long MOD = M) {
  A %= MOD;
  A += MOD;
  A %= MOD;
}
template <typename T>
inline void max_(T &A, T B) {
  (A < B) && (A = B);
}
template <typename T>
inline void min_(T &A, T B) {
  (A > B) && (A = B);
}
template <typename T>
inline T abs(T a) {
  return a > 0 ? a : -a;
}
template <typename T>
inline T powMM(T a, T b) {
  T ret = 1;
  for (; b; b >>= 1ll, a = (long long)a * a % M)
    if (b & 1) ret = (long long)ret * a % M;
  return ret;
}
int startTime;
void startTimer() { startTime = clock(); }
void printTimer() {
  fprintf(stderr, "/--- Time: %ld milliseconds ---/\n", clock() - startTime);
}
int n, m, q;
int A[maxn];
long long val[maxn * 4], lazyval[maxn * 4], bit[307];
long long sum[maxn * 4], lazysum[maxn * 4];
void change(int x, int len, int mul, long long xo) {
  sum[x] = sum[x] * powMM(mul, len) % M;
  lazysum[x] = lazysum[x] * mul % M;
  val[x] = val[x] | xo;
  lazyval[x] |= xo;
}
void pushdown(int x, int L, int mid, int R) {
  if (lazyval[x]) {
    change(x << 1, mid - L + 1, lazysum[x], lazyval[x]);
    change(x << 1 | 1, R - mid, lazysum[x], lazyval[x]);
    lazysum[x] = 1;
    lazyval[x] = 0;
  }
}
void pushup(int x) {
  sum[x] = sum[x << 1] * sum[x << 1 | 1] % M;
  val[x] = val[x << 1] | val[x << 1 | 1];
}
void build(int x, int l, int r) {
  if (l == r) {
    val[x] = bit[A[l]];
    sum[x] = A[l];
    return;
  }
  int mid = (l + r) / 2;
  build(x << 1, l, mid);
  build(x << 1 | 1, mid + 1, r);
  pushup(x);
  lazysum[x] = 1;
}
void update(int x, int l, int r, int v, int L, int R) {
  if (l <= L && R <= r) {
    change(x, R - L + 1, v, bit[v]);
    return;
  }
  int mid = (L + R) / 2;
  pushdown(x, L, mid, R);
  if (l <= mid) update(x << 1, l, r, v, L, mid);
  if (mid < r) update(x << 1 | 1, l, r, v, mid + 1, R);
  pushup(x);
}
pair<long long, long long> merge(pair<long long, long long> A,
                                 pair<long long, long long> B) {
  return make_pair(A.first * B.first % M, A.second | B.second);
}
pair<long long, long long> query(int x, int l, int r, int L, int R) {
  if (l <= L && R <= r) return make_pair(sum[x], val[x]);
  int mid = (L + R) / 2;
  pair<long long, long long> ret = make_pair(1, 0);
  pushdown(x, L, mid, R);
  if (l <= mid) ret = merge(ret, query(x << 1, l, r, L, mid));
  if (mid < r) ret = merge(ret, query(x << 1 | 1, l, r, mid + 1, R));
  pushup(x);
  return ret;
}
int p[1007];
int chk[1007];
int main() {
  int i, j, C = 0;
  for (i = 2; i <= 300; i++)
    if (!bit[i]) {
      for (j = i; j <= 300; j += i) bit[j] |= 1ll << C;
      chk[C] = powMM((long long)i, M - 2) * (i - 1) % M;
      p[C++] = i;
    }
  scanf("%d%d", &n, &q);
  for (i = 1; i <= n; i++) scanf("%d", &A[i]);
  build(1, 1, n);
  while (q--) {
    char op[107];
    scanf("%s", op);
    if (op[0] == 'T') {
      int l, r;
      scanf("%d%d", &l, &r);
      pair<long long, long long> ans = query(1, l, r, 1, n);
      for (i = 0; i < 62; i++)
        if ((ans.second >> i) & 1) ans.first = ans.first * chk[i] % M;
      printf("%lld\n", ans.first);
    } else {
      int l, r, x;
      scanf("%d%d%d", &l, &r, &x);
      update(1, l, r, x, 1, n);
    }
  }
}

```