#include <bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
const int MAX = 1001000;
int n, m, vis[MAX], a[MAX];
long long ret;
vector<int> p[MAX];
struct query {
  int l, r;
  int id;
  bool operator<(const query& A) const { return r < A.r; }
} q[MAX];
long long pow_mod(int a, int b) {
  if (!b) return 1;
  long long ans = pow_mod(a, b / 2);
  ans = (ans * ans) % mod;
  if (b & 1) ans = (ans * a) % mod;
  return ans;
}
long long get_inv(int x) { return pow_mod(x, mod - 2); }
void init(int n) {
  memset(vis, 0, sizeof(vis));
  for (int i = 2; i <= n; i++)
    if (!vis[i]) {
      for (int j = i; j <= n; j += i) {
        vis[j] = 1;
        p[j].push_back(i);
      }
    }
}
int ans[MAX], last[MAX];
long long c[MAX], pre[MAX];
inline int lowbit(int x) { return x & -x; }
void mul(int x, int val) {
  while (x <= n) {
    c[x] = (c[x] * val) % mod;
    x += lowbit(x);
  }
}
long long getmul(int x) {
  ret = 1;
  while (x > 0) {
    ret = (ret * c[x]) % mod;
    x -= lowbit(x);
  }
  return ret;
}
void work() {
  pre[0] = 1;
  int cur = 1;
  memset(last, 0, sizeof(last));
  for (int i = 1; i <= n; i++) c[i] = 1;
  for (int i = 1; i <= n; i++) {
    pre[i] = pre[i - 1] * a[i] % mod;
    for (int j = 0; j < p[a[i]].size(); j++) {
      int tmp = p[a[i]][j];
      if (last[tmp]) {
        mul(last[tmp], tmp);
        mul(last[tmp], get_inv(tmp - 1));
      }
      mul(i, tmp - 1);
      mul(i, get_inv(tmp));
      last[tmp] = i;
    }
    while (cur <= m && q[cur].r == i) {
      ans[q[cur].id] = getmul(i) * get_inv(getmul(q[cur].l - 1)) % mod *
                       pre[i] % mod * get_inv(pre[q[cur].l - 1]) % mod;
      cur++;
    }
  }
}
int main() {
  init(1000010);
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  scanf("%d", &m);
  for (int i = 1; i <= m; i++) {
    scanf("%d%d", &q[i].l, &q[i].r);
    q[i].id = i;
  }
  sort(q + 1, q + 1 + m);
  work();
  for (int i = 1; i <= m; i++) printf("%d\n", ans[i]);
  return 0;
}

### Prompt

Your task is to create 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;
const int mod = 1e9 + 7;
const int MAX = 1001000;
int n, m, vis[MAX], a[MAX];
long long ret;
vector<int> p[MAX];
struct query {
  int l, r;
  int id;
  bool operator<(const query& A) const { return r < A.r; }
} q[MAX];
long long pow_mod(int a, int b) {
  if (!b) return 1;
  long long ans = pow_mod(a, b / 2);
  ans = (ans * ans) % mod;
  if (b & 1) ans = (ans * a) % mod;
  return ans;
}
long long get_inv(int x) { return pow_mod(x, mod - 2); }
void init(int n) {
  memset(vis, 0, sizeof(vis));
  for (int i = 2; i <= n; i++)
    if (!vis[i]) {
      for (int j = i; j <= n; j += i) {
        vis[j] = 1;
        p[j].push_back(i);
      }
    }
}
int ans[MAX], last[MAX];
long long c[MAX], pre[MAX];
inline int lowbit(int x) { return x & -x; }
void mul(int x, int val) {
  while (x <= n) {
    c[x] = (c[x] * val) % mod;
    x += lowbit(x);
  }
}
long long getmul(int x) {
  ret = 1;
  while (x > 0) {
    ret = (ret * c[x]) % mod;
    x -= lowbit(x);
  }
  return ret;
}
void work() {
  pre[0] = 1;
  int cur = 1;
  memset(last, 0, sizeof(last));
  for (int i = 1; i <= n; i++) c[i] = 1;
  for (int i = 1; i <= n; i++) {
    pre[i] = pre[i - 1] * a[i] % mod;
    for (int j = 0; j < p[a[i]].size(); j++) {
      int tmp = p[a[i]][j];
      if (last[tmp]) {
        mul(last[tmp], tmp);
        mul(last[tmp], get_inv(tmp - 1));
      }
      mul(i, tmp - 1);
      mul(i, get_inv(tmp));
      last[tmp] = i;
    }
    while (cur <= m && q[cur].r == i) {
      ans[q[cur].id] = getmul(i) * get_inv(getmul(q[cur].l - 1)) % mod *
                       pre[i] % mod * get_inv(pre[q[cur].l - 1]) % mod;
      cur++;
    }
  }
}
int main() {
  init(1000010);
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  scanf("%d", &m);
  for (int i = 1; i <= m; i++) {
    scanf("%d%d", &q[i].l, &q[i].r);
    q[i].id = i;
  }
  sort(q + 1, q + 1 + m);
  work();
  for (int i = 1; i <= m; i++) printf("%d\n", ans[i]);
  return 0;
}

```