#include <bits/stdc++.h>
using namespace std;
const int N = 2e5 + 10;
const int mod = 1e9 + 7;
int arr[N], b[N], pre[N];
int primes[1000010], tot, f[1000010];
bool check[1000010];
int old[1000010];
int a[N];
int n;
long long qmi(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = ans * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return ans;
}
struct node {
  int l, r, id;
};
node qry[N];
int ans[N];
bool cmp(node a, node b) { return a.r < b.r; }
inline long long inv(int x) { return qmi(x, mod - 2); }
inline int lowbit(int x) { return x & -x; }
inline void add(int x, int d) {
  for (int i = x; i <= n; i += lowbit(i)) {
    b[i] = 1ll * b[i] * d % mod;
  }
}
inline int query(int x) {
  long long ans = 1;
  for (int i = x; i; i -= lowbit(i)) {
    ans = ans * b[i] % mod;
  }
  return ans;
}
inline void update(int x) {
  int val = arr[x];
  for (int p = f[val]; p > 1; p = f[val]) {
    add(x, p - 1), add(x, inv(p));
    if (old[p]) add(old[p], inv(p - 1)), add(old[p], p);
    old[p] = x;
    while (val % p == 0) val /= p;
  }
}
void init(int n) {
  for (int i = 2; i <= n; i++) {
    if (!check[i]) {
      primes[++tot] = i;
      f[i] = i;
    }
    for (int j = 1; primes[j] * i <= n; j++) {
      check[primes[j] * i] = true;
      if (i % primes[j] == 0) {
        f[primes[j] * i] = f[i];
        break;
      }
      f[primes[j] * i] = primes[j];
    }
  }
}
int main() {
  cin >> n;
  init(1000000);
  pre[0] = 1;
  for (int i = 0; i <= n; i++) b[i] = 1;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i];
    pre[i] = 1ll * arr[i] * pre[i - 1] % mod;
  }
  int q;
  cin >> q;
  for (int i = 1; i <= q; i++) {
    cin >> qry[i].l >> qry[i].r;
    qry[i].id = i;
  }
  sort(qry + 1, qry + q + 1, cmp);
  int now = 1;
  for (int i = 1; i <= q; i++) {
    while (now <= qry[i].r) {
      update(now);
      now++;
    }
    int l = qry[i].l, r = qry[i].r;
    ans[qry[i].id] = 1ll * pre[r] * inv(pre[l - 1]) % mod * query(r) % mod *
                     inv(query(l - 1)) % mod;
  }
  for (int i = 1; i <= q; i++) cout << ans[i] << endl;
}

### 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 N = 2e5 + 10;
const int mod = 1e9 + 7;
int arr[N], b[N], pre[N];
int primes[1000010], tot, f[1000010];
bool check[1000010];
int old[1000010];
int a[N];
int n;
long long qmi(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) ans = ans * a % mod;
    a = a * a % mod;
    b >>= 1;
  }
  return ans;
}
struct node {
  int l, r, id;
};
node qry[N];
int ans[N];
bool cmp(node a, node b) { return a.r < b.r; }
inline long long inv(int x) { return qmi(x, mod - 2); }
inline int lowbit(int x) { return x & -x; }
inline void add(int x, int d) {
  for (int i = x; i <= n; i += lowbit(i)) {
    b[i] = 1ll * b[i] * d % mod;
  }
}
inline int query(int x) {
  long long ans = 1;
  for (int i = x; i; i -= lowbit(i)) {
    ans = ans * b[i] % mod;
  }
  return ans;
}
inline void update(int x) {
  int val = arr[x];
  for (int p = f[val]; p > 1; p = f[val]) {
    add(x, p - 1), add(x, inv(p));
    if (old[p]) add(old[p], inv(p - 1)), add(old[p], p);
    old[p] = x;
    while (val % p == 0) val /= p;
  }
}
void init(int n) {
  for (int i = 2; i <= n; i++) {
    if (!check[i]) {
      primes[++tot] = i;
      f[i] = i;
    }
    for (int j = 1; primes[j] * i <= n; j++) {
      check[primes[j] * i] = true;
      if (i % primes[j] == 0) {
        f[primes[j] * i] = f[i];
        break;
      }
      f[primes[j] * i] = primes[j];
    }
  }
}
int main() {
  cin >> n;
  init(1000000);
  pre[0] = 1;
  for (int i = 0; i <= n; i++) b[i] = 1;
  for (int i = 1; i <= n; i++) {
    cin >> arr[i];
    pre[i] = 1ll * arr[i] * pre[i - 1] % mod;
  }
  int q;
  cin >> q;
  for (int i = 1; i <= q; i++) {
    cin >> qry[i].l >> qry[i].r;
    qry[i].id = i;
  }
  sort(qry + 1, qry + q + 1, cmp);
  int now = 1;
  for (int i = 1; i <= q; i++) {
    while (now <= qry[i].r) {
      update(now);
      now++;
    }
    int l = qry[i].l, r = qry[i].r;
    ans[qry[i].id] = 1ll * pre[r] * inv(pre[l - 1]) % mod * query(r) % mod *
                     inv(query(l - 1)) % mod;
  }
  for (int i = 1; i <= q; i++) cout << ans[i] << endl;
}

```