#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
const int MAX = 1e6 + 6;
const int SQN = 350;
int add(int a, int b) {
  int res = a + b;
  if (res >= mod) {
    return res - mod;
  }
  return res;
}
int mult(int a, int b) {
  long long res = a;
  res *= b;
  if (res >= mod) {
    return res % mod;
  }
  return res;
}
int power(int a, int b) {
  int res = 1;
  while (b) {
    if (b & 1) {
      res = mult(res, a);
    }
    a = mult(a, a);
    b >>= 1;
  }
  return res;
}
int n;
int arr[N];
int spf[MAX];
int res[N];
int inv[MAX];
void pre() {
  for (int i = 1; i < MAX; ++i) {
    spf[i] = i;
  }
  for (int i = 2; i < MAX; ++i) {
    if (spf[i] == i) {
      inv[i] = power(i, mod - 2);
      inv[i - 1] = power(i - 1, mod - 2);
      for (int j = i; j < MAX; j += i) {
        spf[j] = i;
      }
    }
  }
}
int q;
int l, r;
set<int> s[N];
vector<pair<int, int> > v[N];
int ans[N];
int lst[MAX];
int bit[N];
void update(int idx, int val) {
  while (idx) {
    bit[idx] = mult(bit[idx], val);
    idx -= idx & -idx;
  }
}
int query(int idx) {
  int res = 1;
  while (idx <= n) {
    res = mult(res, bit[idx]);
    idx += idx & -idx;
  }
  return res;
}
int main() {
  pre();
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &arr[i]);
    bit[i] = 1;
  }
  res[0] = 1;
  for (int i = 1; i <= n; ++i) {
    res[i] = mult(res[i - 1], arr[i]);
  }
  for (int i = 1; i <= n; ++i) {
    set<int> temp;
    int ele = arr[i];
    while (ele > 1) {
      temp.insert(spf[ele]);
      ele /= spf[ele];
    }
    s[i] = temp;
  }
  scanf("%d", &q);
  for (int i = 1; i <= q; ++i) {
    scanf("%d %d", &l, &r);
    ans[i] = mult(res[r], power(res[l - 1], mod - 2));
    v[r].emplace_back(make_pair(l, i));
  }
  for (int i = 1; i <= n; ++i) {
    for (int p : s[i]) {
      update(lst[p], p);
      update(lst[p], inv[p - 1]);
      update(i, inv[p]);
      update(i, p - 1);
      lst[p] = i;
    }
    for (auto it : v[i]) {
      ans[it.second] = mult(ans[it.second], query(it.first));
    }
  }
  for (int i = 1; i <= q; ++i) {
    printf("%d\n", ans[i]);
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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 N = 2e5 + 5;
const int mod = 1e9 + 7;
const int MAX = 1e6 + 6;
const int SQN = 350;
int add(int a, int b) {
  int res = a + b;
  if (res >= mod) {
    return res - mod;
  }
  return res;
}
int mult(int a, int b) {
  long long res = a;
  res *= b;
  if (res >= mod) {
    return res % mod;
  }
  return res;
}
int power(int a, int b) {
  int res = 1;
  while (b) {
    if (b & 1) {
      res = mult(res, a);
    }
    a = mult(a, a);
    b >>= 1;
  }
  return res;
}
int n;
int arr[N];
int spf[MAX];
int res[N];
int inv[MAX];
void pre() {
  for (int i = 1; i < MAX; ++i) {
    spf[i] = i;
  }
  for (int i = 2; i < MAX; ++i) {
    if (spf[i] == i) {
      inv[i] = power(i, mod - 2);
      inv[i - 1] = power(i - 1, mod - 2);
      for (int j = i; j < MAX; j += i) {
        spf[j] = i;
      }
    }
  }
}
int q;
int l, r;
set<int> s[N];
vector<pair<int, int> > v[N];
int ans[N];
int lst[MAX];
int bit[N];
void update(int idx, int val) {
  while (idx) {
    bit[idx] = mult(bit[idx], val);
    idx -= idx & -idx;
  }
}
int query(int idx) {
  int res = 1;
  while (idx <= n) {
    res = mult(res, bit[idx]);
    idx += idx & -idx;
  }
  return res;
}
int main() {
  pre();
  scanf("%d", &n);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &arr[i]);
    bit[i] = 1;
  }
  res[0] = 1;
  for (int i = 1; i <= n; ++i) {
    res[i] = mult(res[i - 1], arr[i]);
  }
  for (int i = 1; i <= n; ++i) {
    set<int> temp;
    int ele = arr[i];
    while (ele > 1) {
      temp.insert(spf[ele]);
      ele /= spf[ele];
    }
    s[i] = temp;
  }
  scanf("%d", &q);
  for (int i = 1; i <= q; ++i) {
    scanf("%d %d", &l, &r);
    ans[i] = mult(res[r], power(res[l - 1], mod - 2));
    v[r].emplace_back(make_pair(l, i));
  }
  for (int i = 1; i <= n; ++i) {
    for (int p : s[i]) {
      update(lst[p], p);
      update(lst[p], inv[p - 1]);
      update(i, inv[p]);
      update(i, p - 1);
      lst[p] = i;
    }
    for (auto it : v[i]) {
      ans[it.second] = mult(ans[it.second], query(it.first));
    }
  }
  for (int i = 1; i <= q; ++i) {
    printf("%d\n", ans[i]);
  }
}

```