#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const double eps = 1e-8;
const double PI = acos(-1.0);
const int MAXN = 2e5 + 5;
const int MAXM = 1e6 + 5;
const int MOD = 1e9 + 7;
int sgn(double x) {
  if (fabs(x) < eps) return 0;
  if (x < 0)
    return -1;
  else
    return 1;
}
long long pw(long long a, long long n, long long mod) {
  long long ret = 1;
  while (n) {
    if (n & 1) ret = ret * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return ret;
}
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
int n, m, a[MAXN];
long long s[MAXN], inv[MAXN], f[MAXM], g[MAXM];
vector<int> p[MAXM], nxt[MAXM];
struct Q {
  int l, r, id;
  void in(int i) {
    scanf("%d%d", &l, &r);
    id = i;
  }
} q[MAXN];
void init() {
  for (int i = 2; i <= 1e6; i++)
    if (!((int)(p[i]).size())) {
      f[i] = (long long)(i - 1) * pw(i, MOD - 2, MOD) % MOD,
      g[i] = pw(f[i], MOD - 2, MOD);
      for (int j = i; j <= 1e6; j += i) p[j].push_back(i);
    }
}
bool cmp(Q a, Q b) {
  if (a.l != b.l)
    return a.l < b.l;
  else
    return a.r < b.r;
}
long long c[MAXN], ans[MAXN];
bool vis[MAXM];
int lowbit(int x) { return x & -x; }
void add(int x, long long v) {
  for (int i = x; i <= n; i += lowbit(i)) c[i] = c[i] * v % MOD;
}
void del(int i) {
  for (auto v : p[a[i]]) {
    add(i, g[v]);
    int j = upper_bound((nxt[v]).begin(), (nxt[v]).end(), i) - nxt[v].begin();
    if (j != ((int)(nxt[v]).size())) add(nxt[v][j], f[v]);
  }
}
long long getSum(int x) {
  long long ret = 1;
  for (int i = x; i; i -= lowbit(i)) ret = ret * c[i] % MOD;
  return ret;
}
int main() {
  init();
  s[0] = inv[0] = 1;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++)
    scanf("%d", &a[i]), s[i] = s[i - 1] * a[i] % MOD,
                        inv[i] = pw(s[i], MOD - 2, MOD);
  scanf("%d", &m);
  for (int i = 1; i <= m; i++) q[i].in(i);
  sort(q + 1, q + 1 + m, cmp);
  for (int i = 1; i <= n; i++) c[i] = 1;
  for (int i = 1; i <= n; i++) {
    for (auto v : p[a[i]]) {
      nxt[v].push_back(i);
      if (!vis[v]) vis[v] = true, add(i, f[v]);
    }
  }
  int L = 1;
  for (int i = 1; i <= m; i++) {
    while (L < q[i].l) del(L++);
    ans[q[i].id] = getSum(q[i].r) * s[q[i].r] % MOD * inv[q[i].l - 1] % MOD;
  }
  for (int i = 1; i <= m; i++) printf("%I64d\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 INF = 0x3f3f3f3f;
const double eps = 1e-8;
const double PI = acos(-1.0);
const int MAXN = 2e5 + 5;
const int MAXM = 1e6 + 5;
const int MOD = 1e9 + 7;
int sgn(double x) {
  if (fabs(x) < eps) return 0;
  if (x < 0)
    return -1;
  else
    return 1;
}
long long pw(long long a, long long n, long long mod) {
  long long ret = 1;
  while (n) {
    if (n & 1) ret = ret * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return ret;
}
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
int n, m, a[MAXN];
long long s[MAXN], inv[MAXN], f[MAXM], g[MAXM];
vector<int> p[MAXM], nxt[MAXM];
struct Q {
  int l, r, id;
  void in(int i) {
    scanf("%d%d", &l, &r);
    id = i;
  }
} q[MAXN];
void init() {
  for (int i = 2; i <= 1e6; i++)
    if (!((int)(p[i]).size())) {
      f[i] = (long long)(i - 1) * pw(i, MOD - 2, MOD) % MOD,
      g[i] = pw(f[i], MOD - 2, MOD);
      for (int j = i; j <= 1e6; j += i) p[j].push_back(i);
    }
}
bool cmp(Q a, Q b) {
  if (a.l != b.l)
    return a.l < b.l;
  else
    return a.r < b.r;
}
long long c[MAXN], ans[MAXN];
bool vis[MAXM];
int lowbit(int x) { return x & -x; }
void add(int x, long long v) {
  for (int i = x; i <= n; i += lowbit(i)) c[i] = c[i] * v % MOD;
}
void del(int i) {
  for (auto v : p[a[i]]) {
    add(i, g[v]);
    int j = upper_bound((nxt[v]).begin(), (nxt[v]).end(), i) - nxt[v].begin();
    if (j != ((int)(nxt[v]).size())) add(nxt[v][j], f[v]);
  }
}
long long getSum(int x) {
  long long ret = 1;
  for (int i = x; i; i -= lowbit(i)) ret = ret * c[i] % MOD;
  return ret;
}
int main() {
  init();
  s[0] = inv[0] = 1;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++)
    scanf("%d", &a[i]), s[i] = s[i - 1] * a[i] % MOD,
                        inv[i] = pw(s[i], MOD - 2, MOD);
  scanf("%d", &m);
  for (int i = 1; i <= m; i++) q[i].in(i);
  sort(q + 1, q + 1 + m, cmp);
  for (int i = 1; i <= n; i++) c[i] = 1;
  for (int i = 1; i <= n; i++) {
    for (auto v : p[a[i]]) {
      nxt[v].push_back(i);
      if (!vis[v]) vis[v] = true, add(i, f[v]);
    }
  }
  int L = 1;
  for (int i = 1; i <= m; i++) {
    while (L < q[i].l) del(L++);
    ans[q[i].id] = getSum(q[i].r) * s[q[i].r] % MOD * inv[q[i].l - 1] % MOD;
  }
  for (int i = 1; i <= m; i++) printf("%I64d\n", ans[i]);
}

```