#include <bits/stdc++.h>
using namespace std;
using namespace std;
const int MAXN = 2e5 + 7;
const int MAXA = 1e6 + 7;
const int MOD = 1e9 + 7;
int n, a[MAXN], whe[MAXA], fen[MAXN];
struct query {
  int l, r, id, sol;
  query() {}
  query(int a, int b) : l(a), r(b) {}
} que[MAXN];
bool compareR(query a, query b) { return a.r < b.r; }
bool compareID(query a, query b) { return a.id < b.id; }
int wop(int x, int y) {
  if (y == 0) return 1;
  int res = wop(x, y >> 1);
  return 1LL * res * res % MOD * (y & 1 ? x : 1) % MOD;
}
int inv(int x) { return wop(x, MOD - 2); }
void upd(int idx, int val) {
  for (; idx <= n; idx += (idx & -idx)) fen[idx] = (1LL * fen[idx] * val) % MOD;
}
int get(int idx) {
  int ret = 1;
  for (; idx; idx -= (idx & -idx)) ret = (1LL * ret * fen[idx]) % MOD;
  return ret;
}
void add(int x, int pos) {
  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0) {
      while (x % i == 0) x /= i;
      if (whe[i] != -1) {
        upd(whe[i], i);
        upd(whe[i], inv(i - 1));
      }
      whe[i] = pos;
      upd(pos, i - 1);
      upd(pos, inv(i));
    }
  if (x > 1) {
    if (whe[x] != -1) {
      upd(whe[x], x);
      upd(whe[x], inv(x - 1));
    }
    whe[x] = pos;
    upd(pos, x - 1);
    upd(pos, inv(x));
  }
}
int main() {
  fill(fen, fen + MAXN, 1);
  memset(whe, -1, sizeof whe);
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
    upd(i, a[i]);
  }
  int q;
  scanf("%d", &q);
  for (int i = 0; i < q; ++i) {
    scanf("%d %d", &que[i].l, &que[i].r);
    que[i].l--;
    que[i].id = i;
  }
  sort(que, que + q, compareR);
  int lst = 1;
  for (int i = 0; i < q; ++i) {
    while (lst <= que[i].r) {
      add(a[lst], lst);
      lst++;
    }
    que[i].sol = (1LL * get(que[i].r) * inv(get(que[i].l))) % MOD;
  }
  sort(que, que + q, compareID);
  for (int i = 0; i < q; ++i) printf("%d\n", que[i].sol);
  return 0;
}

### Prompt

Generate a CPP solution to 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;
using namespace std;
const int MAXN = 2e5 + 7;
const int MAXA = 1e6 + 7;
const int MOD = 1e9 + 7;
int n, a[MAXN], whe[MAXA], fen[MAXN];
struct query {
  int l, r, id, sol;
  query() {}
  query(int a, int b) : l(a), r(b) {}
} que[MAXN];
bool compareR(query a, query b) { return a.r < b.r; }
bool compareID(query a, query b) { return a.id < b.id; }
int wop(int x, int y) {
  if (y == 0) return 1;
  int res = wop(x, y >> 1);
  return 1LL * res * res % MOD * (y & 1 ? x : 1) % MOD;
}
int inv(int x) { return wop(x, MOD - 2); }
void upd(int idx, int val) {
  for (; idx <= n; idx += (idx & -idx)) fen[idx] = (1LL * fen[idx] * val) % MOD;
}
int get(int idx) {
  int ret = 1;
  for (; idx; idx -= (idx & -idx)) ret = (1LL * ret * fen[idx]) % MOD;
  return ret;
}
void add(int x, int pos) {
  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0) {
      while (x % i == 0) x /= i;
      if (whe[i] != -1) {
        upd(whe[i], i);
        upd(whe[i], inv(i - 1));
      }
      whe[i] = pos;
      upd(pos, i - 1);
      upd(pos, inv(i));
    }
  if (x > 1) {
    if (whe[x] != -1) {
      upd(whe[x], x);
      upd(whe[x], inv(x - 1));
    }
    whe[x] = pos;
    upd(pos, x - 1);
    upd(pos, inv(x));
  }
}
int main() {
  fill(fen, fen + MAXN, 1);
  memset(whe, -1, sizeof whe);
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
    upd(i, a[i]);
  }
  int q;
  scanf("%d", &q);
  for (int i = 0; i < q; ++i) {
    scanf("%d %d", &que[i].l, &que[i].r);
    que[i].l--;
    que[i].id = i;
  }
  sort(que, que + q, compareR);
  int lst = 1;
  for (int i = 0; i < q; ++i) {
    while (lst <= que[i].r) {
      add(a[lst], lst);
      lst++;
    }
    que[i].sol = (1LL * get(que[i].r) * inv(get(que[i].l))) % MOD;
  }
  sort(que, que + q, compareID);
  for (int i = 0; i < q; ++i) printf("%d\n", que[i].sol);
  return 0;
}

```