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 int N = 100000 + 10;
long long mpow(long long a, long long n, long long M) {
  if (n == 0) return 1;
  long long t = mpow(a, n / 2, M);
  if (n % 2) return t * t % M * a % M;
  return t * t % M;
}
long long getphi(long long x) {
  long long ans = x;
  for (long long i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      ans = ans * (i - 1) / i;
      while (x % i == 0) x /= i;
    }
  }
  if (x > 1) ans = ans * (x - 1) / x;
  return ans;
}
long long phi[1002];
int n, m;
int w[N], q, l, r;
int lim, cur;
long long mode(long long x, long long y) {
  if (x < y) return x;
  return x % y + y;
}
long long cac(int l, int r, int dep) {
  if (l == r) return w[l];
  if (dep == lim) return 1;
  long long t = cac(l + 1, r, dep + 1);
  long long ans = 1, x = w[l];
  while (t) {
    if (t & 1) ans = mode(ans * x, phi[dep]);
    x = mode(x * x, phi[dep]);
    t >>= 1;
  }
  return ans;
}
int main() {
  scanf("%d %d", &n, &m);
  lim = 0, cur = m;
  phi[0] = m;
  while (m > 1) {
    phi[++lim] = m = getphi(m);
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &w[i]);
  }
  scanf("%d", &q);
  while (q--) {
    scanf("%d %d", &l, &r);
    printf("%lld\n", cac(l, r, 0) % phi[0]);
  }
}