#include <bits/stdc++.h>
int n, m;
int a[200100];
int q[200100][2];
int ers[1001000];
int it[1 << 19];
int mod = 1000000007;
int ans[200100];
int last[1001000];
struct qry {
  int loc;
  int xs, xd;
  bool operator<(const qry& r) const { return xd < r.xd; }
};
qry ql[200100];
long long int mpow(long long int x, long long int y) {
  if (y == 0) return 1;
  long long int d = mpow(x, y / 2);
  d *= d;
  d %= mod;
  if (y % 2 == 1) {
    d *= x;
    d %= mod;
  }
  return d;
}
long long int inv(int x) { return mpow(x, mod - 2); }
void push(int start, int end, long long int val) {
  start += 1 << 18;
  end += 1 << 18;
  while (start <= end) {
    if (start % 2 == 1) {
      it[start] = (it[start] * val) % mod;
      start++;
    }
    if (end % 2 == 0) {
      it[end] = (it[end] * val) % mod;
      end--;
    }
    start /= 2;
    end /= 2;
  }
}
int calc(int x) {
  x += 1 << 18;
  long long int d = 1;
  while (x > 0) {
    d *= it[x];
    d %= mod;
    x /= 2;
  }
  return d;
}
int main() {
  int i, j, k;
  for (i = 1; i < (1 << 19); i++) it[i] = 1;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  scanf("%d", &m);
  for (i = 0; i < m; i++) {
    scanf("%d%d", &q[i][0], &q[i][1]);
    ql[i].loc = i;
    ql[i].xs = q[i][0] - 1;
    ql[i].xd = q[i][1] - 1;
  }
  std::sort(ql, ql + m);
  j = 0;
  for (i = 0; i < n; i++) {
    push(0, i, a[i]);
    for (k = 2; k * k <= a[i]; k++) {
      if (a[i] % k == 0) {
        while (a[i] % k == 0) a[i] /= k;
        push(last[k], i, ((k - 1) * inv(k)) % mod);
        last[k] = i + 1;
      }
    }
    if (a[i] != 1) {
      k = a[i];
      push(last[k], i, ((k - 1) * inv(k)) % mod);
      last[k] = i + 1;
    }
    while (j < m && ql[j].xd == i) {
      ans[ql[j].loc] = calc(ql[j].xs);
      j++;
    }
  }
  for (i = 0; i < m; i++) {
    printf("%d\n", ans[i]);
  }
}

### Prompt

In cpp, your task is to solve 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>
int n, m;
int a[200100];
int q[200100][2];
int ers[1001000];
int it[1 << 19];
int mod = 1000000007;
int ans[200100];
int last[1001000];
struct qry {
  int loc;
  int xs, xd;
  bool operator<(const qry& r) const { return xd < r.xd; }
};
qry ql[200100];
long long int mpow(long long int x, long long int y) {
  if (y == 0) return 1;
  long long int d = mpow(x, y / 2);
  d *= d;
  d %= mod;
  if (y % 2 == 1) {
    d *= x;
    d %= mod;
  }
  return d;
}
long long int inv(int x) { return mpow(x, mod - 2); }
void push(int start, int end, long long int val) {
  start += 1 << 18;
  end += 1 << 18;
  while (start <= end) {
    if (start % 2 == 1) {
      it[start] = (it[start] * val) % mod;
      start++;
    }
    if (end % 2 == 0) {
      it[end] = (it[end] * val) % mod;
      end--;
    }
    start /= 2;
    end /= 2;
  }
}
int calc(int x) {
  x += 1 << 18;
  long long int d = 1;
  while (x > 0) {
    d *= it[x];
    d %= mod;
    x /= 2;
  }
  return d;
}
int main() {
  int i, j, k;
  for (i = 1; i < (1 << 19); i++) it[i] = 1;
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%d", &a[i]);
  }
  scanf("%d", &m);
  for (i = 0; i < m; i++) {
    scanf("%d%d", &q[i][0], &q[i][1]);
    ql[i].loc = i;
    ql[i].xs = q[i][0] - 1;
    ql[i].xd = q[i][1] - 1;
  }
  std::sort(ql, ql + m);
  j = 0;
  for (i = 0; i < n; i++) {
    push(0, i, a[i]);
    for (k = 2; k * k <= a[i]; k++) {
      if (a[i] % k == 0) {
        while (a[i] % k == 0) a[i] /= k;
        push(last[k], i, ((k - 1) * inv(k)) % mod);
        last[k] = i + 1;
      }
    }
    if (a[i] != 1) {
      k = a[i];
      push(last[k], i, ((k - 1) * inv(k)) % mod);
      last[k] = i + 1;
    }
    while (j < m && ql[j].xd == i) {
      ans[ql[j].loc] = calc(ql[j].xs);
      j++;
    }
  }
  for (i = 0; i < m; i++) {
    printf("%d\n", ans[i]);
  }
}

```