#include <bits/stdc++.h>
using namespace std;
namespace ProconLib {
template <typename update_t, typename value_t>
class LazySegmentTree {
 public:
  using UpdateMerger = std::function<update_t(update_t, update_t)>;
  using ValueMerger = std::function<value_t(value_t, value_t)>;
  using Evaluator = std::function<value_t(value_t, update_t, int, int)>;

 private:
  int N;
  const value_t E;
  UpdateMerger mergeU;
  ValueMerger mergeV;
  Evaluator eval;
  std::vector<value_t> dat;
  std::vector<update_t> lazy;
  std::vector<int> flag;
  void propagate(int node, int l, int r);
  void applyLazy(int node, update_t x);
  void updateImpl(int l, int r, int k, int lb, int ub, update_t f);
  value_t queryImpl(int l, int r, int k, int lb, int ub);
  value_t getValue(int node, int l, int r) {
    return flag[node] ? eval(dat[node], lazy[node], l, r) : dat[node];
  }

 public:
  LazySegmentTree(int N, Evaluator eval, UpdateMerger mergeU,
                  ValueMerger mergeV, value_t E);
  void update(int l, int r, update_t f);
  value_t query(int a, int b);
};
template <typename update_t, typename value_t>
LazySegmentTree<update_t, value_t>::LazySegmentTree(int N, Evaluator eval,
                                                    UpdateMerger mergeU,
                                                    ValueMerger mergeV,
                                                    value_t E)
    : mergeU(mergeU), mergeV(mergeV), eval(eval), E(E) {
  this->N = 1;
  while (this->N < N) this->N *= 2;
  dat.assign(this->N * 2 - 1, E);
  lazy.assign(this->N * 2 - 1, update_t());
  flag.assign(this->N * 2 - 1, false);
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::propagate(int node, int l, int r) {
  if (flag[node]) {
    flag[node] = false;
    applyLazy(node * 2 + 1, lazy[node]);
    applyLazy(node * 2 + 2, lazy[node]);
    int mid = (l + r) / 2;
    dat[node] =
        mergeV(getValue(node * 2 + 1, l, mid), getValue(node * 2 + 2, mid, r));
  }
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::applyLazy(int node, update_t x) {
  if (flag[node]) {
    lazy[node] = mergeU(lazy[node], x);
  } else {
    flag[node] = true;
    lazy[node] = x;
  }
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::updateImpl(int l, int r, int k, int lb,
                                                    int ub, update_t x) {
  if (r <= lb || ub <= l) return;
  if (l <= lb && ub <= r) {
    applyLazy(k, x);
    return;
  }
  propagate(k, lb, ub);
  int mid = (lb + ub) / 2;
  updateImpl(l, r, k * 2 + 1, lb, mid, x);
  updateImpl(l, r, k * 2 + 2, mid, ub, x);
  dat[k] = mergeV(getValue(k * 2 + 1, lb, mid), getValue(k * 2 + 2, mid, ub));
}
template <typename update_t, typename value_t>
value_t LazySegmentTree<update_t, value_t>::queryImpl(int l, int r, int k,
                                                      int lb, int ub) {
  if (r <= lb || ub <= l) return E;
  if (l <= lb && ub <= r) {
    return getValue(k, lb, ub);
  }
  propagate(k, lb, ub);
  int mid = (lb + ub) / 2;
  value_t lhs = queryImpl(l, r, k * 2 + 1, lb, mid);
  value_t rhs = queryImpl(l, r, k * 2 + 2, mid, ub);
  return mergeV(lhs, rhs);
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::update(int l, int r, update_t x) {
  updateImpl(l, r, 0, 0, N, x);
}
template <typename update_t, typename value_t>
value_t LazySegmentTree<update_t, value_t>::query(int l, int r) {
  return queryImpl(l, r, 0, 0, N);
}
}  // namespace ProconLib
using namespace ProconLib;
using ll = long long;
const int SIZE = 300;
const int PSIZE = 64;
using Flags = bitset<PSIZE>;
const ll MOD = 1e9 + 7;
ll powm(ll x, ll k) {
  ll res = 1;
  while (k) {
    if (k & 1) res = res * x % MOD;
    k >>= 1;
    x = x * x % MOD;
  }
  return res;
}
ll mulEval(ll a, ll x, int l, int r) { return a * powm(x, r - l) % MOD; }
ll mul(ll a, ll b) { return a * b % MOD; }
Flags fmerge(Flags lhs, Flags rhs) { return lhs | rhs; }
Flags fmergeEval(Flags lhs, Flags rhs, int l, int r) { return lhs | rhs; }
ll modInv(ll x) { return powm(x, MOD - 2); }
int main() {
  vector<int> primes;
  for (int i = 2; i <= SIZE; i++) {
    bool isPrime = true;
    for (int j = 2; j < i; j++) {
      if (i % j == 0) {
        isPrime = false;
        break;
      }
    }
    if (isPrime) primes.push_back(i);
  }
  int n, q;
  cin >> n >> q;
  vector<ll> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  LazySegmentTree<ll, ll> mulSeg(n, mulEval, mul, mul, 1);
  for (int i = 0; i < n; i++) mulSeg.update(i, i + 1, a[i]);
  LazySegmentTree<Flags, Flags> pSeg(n, fmergeEval, fmerge, fmerge, Flags());
  vector<Flags> pa(n);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < primes.size(); j++) {
      if (a[i] % primes[j] == 0) pa[i][j] = true;
    }
  for (int i = 0; i < n; i++) pSeg.update(i, i + 1, pa[i]);
  vector<ll> primeInv(primes.size());
  transform(primes.begin(), primes.end(), primeInv.begin(), modInv);
  while (q--) {
    string query;
    cin >> query;
    if (query == "MULTIPLY") {
      int l, r, x;
      cin >> l >> r >> x;
      l--;
      mulSeg.update(l, r, x);
      Flags app;
      for (int j = 0; j < primes.size(); j++) {
        if (x % primes[j] == 0) app[j] = true;
      }
      pSeg.update(l, r, app);
    } else {
      int l, r;
      cin >> l >> r;
      l--;
      Flags flags = pSeg.query(l, r);
      ll res = mulSeg.query(l, r);
      for (int i = 0; i < primes.size(); i++)
        if (flags[i]) res = res * (primes[i] - 1) % MOD * primeInv[i] % MOD;
      cout << res << endl;
    }
  }
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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;
namespace ProconLib {
template <typename update_t, typename value_t>
class LazySegmentTree {
 public:
  using UpdateMerger = std::function<update_t(update_t, update_t)>;
  using ValueMerger = std::function<value_t(value_t, value_t)>;
  using Evaluator = std::function<value_t(value_t, update_t, int, int)>;

 private:
  int N;
  const value_t E;
  UpdateMerger mergeU;
  ValueMerger mergeV;
  Evaluator eval;
  std::vector<value_t> dat;
  std::vector<update_t> lazy;
  std::vector<int> flag;
  void propagate(int node, int l, int r);
  void applyLazy(int node, update_t x);
  void updateImpl(int l, int r, int k, int lb, int ub, update_t f);
  value_t queryImpl(int l, int r, int k, int lb, int ub);
  value_t getValue(int node, int l, int r) {
    return flag[node] ? eval(dat[node], lazy[node], l, r) : dat[node];
  }

 public:
  LazySegmentTree(int N, Evaluator eval, UpdateMerger mergeU,
                  ValueMerger mergeV, value_t E);
  void update(int l, int r, update_t f);
  value_t query(int a, int b);
};
template <typename update_t, typename value_t>
LazySegmentTree<update_t, value_t>::LazySegmentTree(int N, Evaluator eval,
                                                    UpdateMerger mergeU,
                                                    ValueMerger mergeV,
                                                    value_t E)
    : mergeU(mergeU), mergeV(mergeV), eval(eval), E(E) {
  this->N = 1;
  while (this->N < N) this->N *= 2;
  dat.assign(this->N * 2 - 1, E);
  lazy.assign(this->N * 2 - 1, update_t());
  flag.assign(this->N * 2 - 1, false);
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::propagate(int node, int l, int r) {
  if (flag[node]) {
    flag[node] = false;
    applyLazy(node * 2 + 1, lazy[node]);
    applyLazy(node * 2 + 2, lazy[node]);
    int mid = (l + r) / 2;
    dat[node] =
        mergeV(getValue(node * 2 + 1, l, mid), getValue(node * 2 + 2, mid, r));
  }
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::applyLazy(int node, update_t x) {
  if (flag[node]) {
    lazy[node] = mergeU(lazy[node], x);
  } else {
    flag[node] = true;
    lazy[node] = x;
  }
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::updateImpl(int l, int r, int k, int lb,
                                                    int ub, update_t x) {
  if (r <= lb || ub <= l) return;
  if (l <= lb && ub <= r) {
    applyLazy(k, x);
    return;
  }
  propagate(k, lb, ub);
  int mid = (lb + ub) / 2;
  updateImpl(l, r, k * 2 + 1, lb, mid, x);
  updateImpl(l, r, k * 2 + 2, mid, ub, x);
  dat[k] = mergeV(getValue(k * 2 + 1, lb, mid), getValue(k * 2 + 2, mid, ub));
}
template <typename update_t, typename value_t>
value_t LazySegmentTree<update_t, value_t>::queryImpl(int l, int r, int k,
                                                      int lb, int ub) {
  if (r <= lb || ub <= l) return E;
  if (l <= lb && ub <= r) {
    return getValue(k, lb, ub);
  }
  propagate(k, lb, ub);
  int mid = (lb + ub) / 2;
  value_t lhs = queryImpl(l, r, k * 2 + 1, lb, mid);
  value_t rhs = queryImpl(l, r, k * 2 + 2, mid, ub);
  return mergeV(lhs, rhs);
}
template <typename update_t, typename value_t>
void LazySegmentTree<update_t, value_t>::update(int l, int r, update_t x) {
  updateImpl(l, r, 0, 0, N, x);
}
template <typename update_t, typename value_t>
value_t LazySegmentTree<update_t, value_t>::query(int l, int r) {
  return queryImpl(l, r, 0, 0, N);
}
}  // namespace ProconLib
using namespace ProconLib;
using ll = long long;
const int SIZE = 300;
const int PSIZE = 64;
using Flags = bitset<PSIZE>;
const ll MOD = 1e9 + 7;
ll powm(ll x, ll k) {
  ll res = 1;
  while (k) {
    if (k & 1) res = res * x % MOD;
    k >>= 1;
    x = x * x % MOD;
  }
  return res;
}
ll mulEval(ll a, ll x, int l, int r) { return a * powm(x, r - l) % MOD; }
ll mul(ll a, ll b) { return a * b % MOD; }
Flags fmerge(Flags lhs, Flags rhs) { return lhs | rhs; }
Flags fmergeEval(Flags lhs, Flags rhs, int l, int r) { return lhs | rhs; }
ll modInv(ll x) { return powm(x, MOD - 2); }
int main() {
  vector<int> primes;
  for (int i = 2; i <= SIZE; i++) {
    bool isPrime = true;
    for (int j = 2; j < i; j++) {
      if (i % j == 0) {
        isPrime = false;
        break;
      }
    }
    if (isPrime) primes.push_back(i);
  }
  int n, q;
  cin >> n >> q;
  vector<ll> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  LazySegmentTree<ll, ll> mulSeg(n, mulEval, mul, mul, 1);
  for (int i = 0; i < n; i++) mulSeg.update(i, i + 1, a[i]);
  LazySegmentTree<Flags, Flags> pSeg(n, fmergeEval, fmerge, fmerge, Flags());
  vector<Flags> pa(n);
  for (int i = 0; i < n; i++)
    for (int j = 0; j < primes.size(); j++) {
      if (a[i] % primes[j] == 0) pa[i][j] = true;
    }
  for (int i = 0; i < n; i++) pSeg.update(i, i + 1, pa[i]);
  vector<ll> primeInv(primes.size());
  transform(primes.begin(), primes.end(), primeInv.begin(), modInv);
  while (q--) {
    string query;
    cin >> query;
    if (query == "MULTIPLY") {
      int l, r, x;
      cin >> l >> r >> x;
      l--;
      mulSeg.update(l, r, x);
      Flags app;
      for (int j = 0; j < primes.size(); j++) {
        if (x % primes[j] == 0) app[j] = true;
      }
      pSeg.update(l, r, app);
    } else {
      int l, r;
      cin >> l >> r;
      l--;
      Flags flags = pSeg.query(l, r);
      ll res = mulSeg.query(l, r);
      for (int i = 0; i < primes.size(); i++)
        if (flags[i]) res = res * (primes[i] - 1) % MOD * primeInv[i] % MOD;
      cout << res << endl;
    }
  }
  return 0;
}

```