#include <bits/stdc++.h>
using namespace std;
const int M = 1000000007;
struct segtree {
  segtree *left = nullptr, *right = nullptr;
  int product;
  void push() {
    if (left == nullptr) {
      left = new segtree();
      right = new segtree();
    }
  }
  void update(int a, int x, int l, int r) {
    if (l == r) {
      product = x;
    } else {
      push();
      int m = (l + r) / 2;
      if (a <= m) {
        left->update(a, x, l, m);
      } else {
        right->update(a, x, m + 1, r);
      }
      product = (long long)left->product * right->product % M;
    }
  }
  int query(int a, int b, int l, int r) {
    if (b < l || r < a) {
      return 1;
    } else if (a <= l && r <= b) {
      return product;
    } else {
      push();
      int m = (l + r) / 2;
      return (long long)left->query(a, b, l, m) * right->query(a, b, m + 1, r) %
             M;
    }
  }
};
const int A = 1000000 + 1;
const int N = 200000 + 1;
int sieve[A], prv[A], ans[N], a[N];
vector<array<int, 2>> queries[N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  for (int i = 2; i < A; ++i) {
    if (sieve[i] == 0) {
      for (int j = i; j < A; j += i) {
        sieve[j] = i;
      }
    }
  }
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int l, r;
    cin >> l >> r;
    queries[r].push_back({l, i});
  }
  segtree *vovo = new segtree();
  for (int i = 1; i <= n; ++i) {
    int x = a[i];
    while (x > 1) {
      int p = sieve[x];
      while (x % p == 0) {
        x /= p;
      }
      a[i] /= p;
      a[i] *= p - 1;
      if (prv[p] != 0) {
        a[prv[p]] /= p - 1;
        a[prv[p]] *= p;
        vovo->update(prv[p], a[prv[p]], 1, n);
      }
      prv[p] = i;
    }
    vovo->update(i, a[i], 1, n);
    for (auto [j, id] : queries[i]) {
      ans[id] = vovo->query(j, i, 1, n);
    }
  }
  for (int i = 0; i < q; ++i) {
    cout << ans[i] << "\n";
  }
}

### Prompt

Create a solution in CPP for the following problem:

Today on a math lesson the teacher told Vovochka that the Euler function of a positive integer φ(n) is an arithmetic function that counts the positive integers less than or equal to n that are relatively prime to n. The number 1 is coprime to all the positive integers and φ(1) = 1.

Now the teacher gave Vovochka an array of n positive integers a1, a2, ..., an and a task to process q queries li ri — to calculate and print <image> modulo 109 + 7. As it is too hard for a second grade school student, you've decided to help Vovochka.

Input

The first line of the input contains number n (1 ≤ n ≤ 200 000) — the length of the array given to Vovochka. The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106).

The third line contains integer q (1 ≤ q ≤ 200 000) — the number of queries. Next q lines contain the queries, one per line. Each query is defined by the boundaries of the segment li and ri (1 ≤ li ≤ ri ≤ n).

Output

Print q numbers — the value of the Euler function for each query, calculated modulo 109 + 7.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10
7
1 1
3 8
5 6
4 8
8 10
7 9
7 10


Output

1
4608
8
1536
192
144
1152


Input

7
24 63 13 52 6 10 1
6
3 5
4 7
1 7
2 4
3 6
2 6


Output

1248
768
12939264
11232
9984
539136

Note

In the second sample the values are calculated like that:

  * φ(13·52·6) = φ(4056) = 1248
  * φ(52·6·10·1) = φ(3120) = 768
  * φ(24·63·13·52·6·10·1) = φ(61326720) = 12939264
  * φ(63·13·52) = φ(42588) = 11232
  * φ(13·52·6·10) = φ(40560) = 9984
  * φ(63·13·52·6·10) = φ(2555280) = 539136

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int M = 1000000007;
struct segtree {
  segtree *left = nullptr, *right = nullptr;
  int product;
  void push() {
    if (left == nullptr) {
      left = new segtree();
      right = new segtree();
    }
  }
  void update(int a, int x, int l, int r) {
    if (l == r) {
      product = x;
    } else {
      push();
      int m = (l + r) / 2;
      if (a <= m) {
        left->update(a, x, l, m);
      } else {
        right->update(a, x, m + 1, r);
      }
      product = (long long)left->product * right->product % M;
    }
  }
  int query(int a, int b, int l, int r) {
    if (b < l || r < a) {
      return 1;
    } else if (a <= l && r <= b) {
      return product;
    } else {
      push();
      int m = (l + r) / 2;
      return (long long)left->query(a, b, l, m) * right->query(a, b, m + 1, r) %
             M;
    }
  }
};
const int A = 1000000 + 1;
const int N = 200000 + 1;
int sieve[A], prv[A], ans[N], a[N];
vector<array<int, 2>> queries[N];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  for (int i = 2; i < A; ++i) {
    if (sieve[i] == 0) {
      for (int j = i; j < A; j += i) {
        sieve[j] = i;
      }
    }
  }
  int n;
  cin >> n;
  for (int i = 1; i <= n; ++i) {
    cin >> a[i];
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; ++i) {
    int l, r;
    cin >> l >> r;
    queries[r].push_back({l, i});
  }
  segtree *vovo = new segtree();
  for (int i = 1; i <= n; ++i) {
    int x = a[i];
    while (x > 1) {
      int p = sieve[x];
      while (x % p == 0) {
        x /= p;
      }
      a[i] /= p;
      a[i] *= p - 1;
      if (prv[p] != 0) {
        a[prv[p]] /= p - 1;
        a[prv[p]] *= p;
        vovo->update(prv[p], a[prv[p]], 1, n);
      }
      prv[p] = i;
    }
    vovo->update(i, a[i], 1, n);
    for (auto [j, id] : queries[i]) {
      ans[id] = vovo->query(j, i, 1, n);
    }
  }
  for (int i = 0; i < q; ++i) {
    cout << ans[i] << "\n";
  }
}

```