#include <bits/stdc++.h>
using namespace std;
const int MAXN = 200000 + 10;
const int MAXV = 1000000 + 100;
const int MOD = 1e9 + 7;
vector<pair<int, int> > ask[MAXN];
int n;
int a[MAXN], pre[MAXV];
int c[MAXN], fac[MAXN];
int ans[MAXN];
int pow_mod(int a, int b) {
  int res = 1;
  while (b) {
    if (b & 1) res = 1LL * res * a % MOD;
    a = 1LL * a * a % MOD;
    b >>= 1;
  }
  return res;
}
int inv(int x) { return pow_mod(x, MOD - 2); }
inline int lowbit(int x) { return x & -x; }
void add(int x, int d) {
  if (!x) {
    return;
  }
  while (x <= n) {
    c[x] = 1LL * c[x] * d % MOD;
    x += lowbit(x);
  }
}
int query(int x) {
  int res = 1;
  while (x > 0) {
    res = 1LL * res * c[x] % MOD;
    x -= lowbit(x);
  }
  return res;
}
int main(int argc, char const *argv[]) {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    c[i] = 1;
  }
  fac[0] = 1;
  for (int i = 1; i <= n; i++) {
    scanf("%d", a + i);
    fac[i] = 1LL * fac[i - 1] * a[i] % MOD;
  }
  int q;
  scanf("%d", &q);
  for (int i = 1; i <= q; i++) {
    int l, r;
    scanf("%d %d", &l, &r);
    ask[r].push_back(pair<int, int>(l, i));
  }
  for (int i = 1; i <= n; i++) {
    int tmp = a[i];
    for (int j = 2; j * j <= tmp; j++)
      if (!(tmp % j)) {
        do {
          tmp /= j;
        } while (!(tmp % j));
        add(i, 1LL * (j - 1) * inv(j) % MOD);
        add(pre[j], inv(1LL * (j - 1) * inv(j) % MOD));
        pre[j] = i;
      }
    if (tmp != 1) {
      add(i, 1LL * (tmp - 1) * inv(tmp) % MOD);
      add(pre[tmp], inv(1LL * (tmp - 1) * inv(tmp) % MOD));
      pre[tmp] = i;
    }
    for (int j = 0; j < ask[i].size(); j++) {
      int t = ask[i][j].first;
      ans[ask[i][j].second] =
          (((1LL * fac[i] * inv(fac[t - 1]) % MOD) * query(i) % MOD) *
           inv(query(t - 1))) %
          MOD;
    }
  }
  for (int i = 1; i <= q; i++) {
    cout << ans[i] << endl;
  }
  return 0;
}

### 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 MAXN = 200000 + 10;
const int MAXV = 1000000 + 100;
const int MOD = 1e9 + 7;
vector<pair<int, int> > ask[MAXN];
int n;
int a[MAXN], pre[MAXV];
int c[MAXN], fac[MAXN];
int ans[MAXN];
int pow_mod(int a, int b) {
  int res = 1;
  while (b) {
    if (b & 1) res = 1LL * res * a % MOD;
    a = 1LL * a * a % MOD;
    b >>= 1;
  }
  return res;
}
int inv(int x) { return pow_mod(x, MOD - 2); }
inline int lowbit(int x) { return x & -x; }
void add(int x, int d) {
  if (!x) {
    return;
  }
  while (x <= n) {
    c[x] = 1LL * c[x] * d % MOD;
    x += lowbit(x);
  }
}
int query(int x) {
  int res = 1;
  while (x > 0) {
    res = 1LL * res * c[x] % MOD;
    x -= lowbit(x);
  }
  return res;
}
int main(int argc, char const *argv[]) {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    c[i] = 1;
  }
  fac[0] = 1;
  for (int i = 1; i <= n; i++) {
    scanf("%d", a + i);
    fac[i] = 1LL * fac[i - 1] * a[i] % MOD;
  }
  int q;
  scanf("%d", &q);
  for (int i = 1; i <= q; i++) {
    int l, r;
    scanf("%d %d", &l, &r);
    ask[r].push_back(pair<int, int>(l, i));
  }
  for (int i = 1; i <= n; i++) {
    int tmp = a[i];
    for (int j = 2; j * j <= tmp; j++)
      if (!(tmp % j)) {
        do {
          tmp /= j;
        } while (!(tmp % j));
        add(i, 1LL * (j - 1) * inv(j) % MOD);
        add(pre[j], inv(1LL * (j - 1) * inv(j) % MOD));
        pre[j] = i;
      }
    if (tmp != 1) {
      add(i, 1LL * (tmp - 1) * inv(tmp) % MOD);
      add(pre[tmp], inv(1LL * (tmp - 1) * inv(tmp) % MOD));
      pre[tmp] = i;
    }
    for (int j = 0; j < ask[i].size(); j++) {
      int t = ask[i][j].first;
      ans[ask[i][j].second] =
          (((1LL * fac[i] * inv(fac[t - 1]) % MOD) * query(i) % MOD) *
           inv(query(t - 1))) %
          MOD;
    }
  }
  for (int i = 1; i <= q; i++) {
    cout << ans[i] << endl;
  }
  return 0;
}

```