#include <bits/stdc++.h>
using namespace std;
constexpr int N = 1e6 + 10;
constexpr int MOD = 1e9 + 7;
long long n, a[N], q, tree[4 * N], pos, ans[N];
pair<int, pair<int, int>> interval[N];
vector<int> p[N];
bool cmp(pair<int, pair<int, int>> lhs, pair<int, pair<int, int>> rhs) {
  return lhs.second.second < rhs.second.second;
}
long long mypow(long long a, long long b) {
  return b ? (mypow(a * a % MOD, b >> 1) * ((b & 1) ? a : 1)) % MOD : 1;
}
void update(int b, int e, int id, int val, int idx) {
  if (id < b || e <= id) return;
  if (b + 1 == e) {
    tree[idx] *= val;
    return;
  }
  int mid = (b + e) >> 1, lidx = idx << 1, ridx = lidx | 1;
  update(b, mid, id, val, lidx);
  update(mid, e, id, val, ridx);
  tree[idx] = (tree[lidx] * tree[ridx]) % MOD;
}
void update2(int b, int e, int id, int val, int idx) {
  if (id < b || e <= id) return;
  if (b + 1 == e) {
    tree[idx] = ((((val + 1) * tree[idx]) % MOD) * mypow(val, MOD - 2)) % MOD;
    return;
  }
  int mid = (b + e) >> 1, lidx = idx << 1, ridx = lidx | 1;
  update2(b, mid, id, val, lidx);
  update2(mid, e, id, val, ridx);
  tree[idx] = (tree[lidx] * tree[ridx]) % MOD;
}
void upd(int pos, int num) {
  for (int i = 2; i * i <= num; i++) {
    if (num % i == 0) {
      long long z = 1;
      while (num % i == 0) {
        num /= i;
        z *= i;
      }
      z /= i;
      if (p[i].size()) update2(1, n + 1, p[i][p[i].size() - 1], i - 1, 1);
      update(1, n + 1, pos, (z * (i - 1)) % MOD, 1);
      p[i].push_back(pos);
    }
  }
  if (num > 1) {
    if (p[num].size()) update2(1, n + 1, p[num][p[num].size() - 1], num - 1, 1);
    update(1, n + 1, pos, num - 1, 1);
    p[num].push_back(pos);
  }
}
long long query(int b, int e, int l, int r, int idx) {
  if (b > r || e <= l) return 1;
  if (b >= l && (e - 1) <= r) return tree[idx];
  int mid = (b + e) >> 1, lidx = idx << 1, ridx = lidx | 1;
  return (query(b, mid, l, r, lidx) * query(mid, e, l, r, ridx)) % MOD;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 0; i < 4 * N; i++) tree[i] = 1;
  cin >> q;
  for (int i = 0; i < q; i++) {
    cin >> interval[i].second.first >> interval[i].second.second;
    interval[i].first = i;
  }
  sort(interval, interval + q, cmp);
  for (int i = 1; i <= n; i++) {
    upd(i, a[i]);
    while (interval[pos].second.second == i) {
      ans[interval[pos].first] = query(1, n + 1, interval[pos].second.first,
                                       interval[pos].second.second, 1);
      pos++;
    }
  }
  for (int i = 0; i < q; i++) cout << ans[i] << '\n';
  return 0;
}

### 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>
using namespace std;
constexpr int N = 1e6 + 10;
constexpr int MOD = 1e9 + 7;
long long n, a[N], q, tree[4 * N], pos, ans[N];
pair<int, pair<int, int>> interval[N];
vector<int> p[N];
bool cmp(pair<int, pair<int, int>> lhs, pair<int, pair<int, int>> rhs) {
  return lhs.second.second < rhs.second.second;
}
long long mypow(long long a, long long b) {
  return b ? (mypow(a * a % MOD, b >> 1) * ((b & 1) ? a : 1)) % MOD : 1;
}
void update(int b, int e, int id, int val, int idx) {
  if (id < b || e <= id) return;
  if (b + 1 == e) {
    tree[idx] *= val;
    return;
  }
  int mid = (b + e) >> 1, lidx = idx << 1, ridx = lidx | 1;
  update(b, mid, id, val, lidx);
  update(mid, e, id, val, ridx);
  tree[idx] = (tree[lidx] * tree[ridx]) % MOD;
}
void update2(int b, int e, int id, int val, int idx) {
  if (id < b || e <= id) return;
  if (b + 1 == e) {
    tree[idx] = ((((val + 1) * tree[idx]) % MOD) * mypow(val, MOD - 2)) % MOD;
    return;
  }
  int mid = (b + e) >> 1, lidx = idx << 1, ridx = lidx | 1;
  update2(b, mid, id, val, lidx);
  update2(mid, e, id, val, ridx);
  tree[idx] = (tree[lidx] * tree[ridx]) % MOD;
}
void upd(int pos, int num) {
  for (int i = 2; i * i <= num; i++) {
    if (num % i == 0) {
      long long z = 1;
      while (num % i == 0) {
        num /= i;
        z *= i;
      }
      z /= i;
      if (p[i].size()) update2(1, n + 1, p[i][p[i].size() - 1], i - 1, 1);
      update(1, n + 1, pos, (z * (i - 1)) % MOD, 1);
      p[i].push_back(pos);
    }
  }
  if (num > 1) {
    if (p[num].size()) update2(1, n + 1, p[num][p[num].size() - 1], num - 1, 1);
    update(1, n + 1, pos, num - 1, 1);
    p[num].push_back(pos);
  }
}
long long query(int b, int e, int l, int r, int idx) {
  if (b > r || e <= l) return 1;
  if (b >= l && (e - 1) <= r) return tree[idx];
  int mid = (b + e) >> 1, lidx = idx << 1, ridx = lidx | 1;
  return (query(b, mid, l, r, lidx) * query(mid, e, l, r, ridx)) % MOD;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  for (int i = 1; i <= n; i++) cin >> a[i];
  for (int i = 0; i < 4 * N; i++) tree[i] = 1;
  cin >> q;
  for (int i = 0; i < q; i++) {
    cin >> interval[i].second.first >> interval[i].second.second;
    interval[i].first = i;
  }
  sort(interval, interval + q, cmp);
  for (int i = 1; i <= n; i++) {
    upd(i, a[i]);
    while (interval[pos].second.second == i) {
      ans[interval[pos].first] = query(1, n + 1, interval[pos].second.first,
                                       interval[pos].second.second, 1);
      pos++;
    }
  }
  for (int i = 0; i < q; i++) cout << ans[i] << '\n';
  return 0;
}

```