Problem: Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from k - 1 rocks, possesses power p and we want to add the rock charged with power wk then value of power of a new tower will be {wk}p. 

Rocks are added from the last to the first. That is for sequence w1, ..., wm value of power will be

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After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo m. Priests have n rocks numbered from 1 to n. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered l, l + 1, ..., r. 

Input

First line of input contains two integers n (1 ≤ n ≤ 105) and m (1 ≤ m ≤ 109).

Second line of input contains n integers wk (1 ≤ wk ≤ 109) which is the power of rocks that priests have.

Third line of input contains single integer q (1 ≤ q ≤ 105) which is amount of queries from priests to you.

kth of next q lines contains two integers lk and rk (1 ≤ lk ≤ rk ≤ n). 

Output

Output q integers. k-th of them must be the amount of cumulative power the tower will have if is built from rocks lk, lk + 1, ..., rk.

Example

Input

6 1000000000
1 2 2 3 3 3
8
1 1
1 6
2 2
2 3
2 4
4 4
4 5
4 6


Output

1
1
2
4
256
3
27
597484987

Note

327 = 7625597484987

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1e9 + 7;
const int maxn = 1e5 + 9;
long long rd() {
  long long ans = 0;
  char last = ' ', ch = getchar();
  while (!(ch >= '0' && ch <= '9')) last = ch, ch = getchar();
  while (ch >= '0' && ch <= '9') ans = ans * 10 + ch - '0', ch = getchar();
  if (last == '-') ans = -ans;
  return ans;
}
long long a[maxn];
unordered_map<int, int> M;
int phi(int x) {
  int res = x, pos = x;
  if (M.count(x)) return M[x];
  for (int i = 2; i <= sqrt(x); i++) {
    if (!(x % i)) {
      res = res / i * (i - 1);
      while (!(x % i)) x /= i;
    }
  }
  if (x > 1) res = res / x * (x - 1);
  return M[pos] = res;
}
long long mo(long long x, long long p) { return x < p ? x : (x % p + p); }
long long Pow(long long a, long long b, long long mod) {
  long long res = 1;
  while (b) {
    if (b & 1) res = mo(res * a, mod);
    a = mo(a * a, mod);
    b >>= 1;
  }
  return res;
}
long long dfs(int l, int r, long long mod) {
  return (l == r || mod == 1) ? mo(a[l], mod)
                              : Pow(a[l], dfs(l + 1, r, phi(mod)), mod);
}
int main() {
  int n = rd(), mod = rd();
  for (int i = (int)(1); i <= (int)(n); i++) a[i] = rd();
  int m = rd();
  while (m--) {
    int l = rd(), r = rd();
    printf("%lld\n", dfs(l, r, mod) % mod);
  }
  return 0;
}