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 maxn = 100005;
int n, m, tot, phi[maxn], w[maxn], q;
int ksm(int x, int n, int m) {
  int ret = 1;
  while (n) {
    if (n & 1) {
      if (1LL * ret * x >= m)
        ret = 1LL * ret * x % m + m;
      else
        ret = ret * x;
    }
    if (1LL * x * x >= m)
      x = 1LL * x * x % m + m;
    else
      x = x * x;
    n >>= 1;
  }
  return ret;
}
inline int Phi(int n) {
  int res = n;
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) {
      res = res / i * (i - 1);
      while (n % i == 0) n /= i;
    }
  if (n > 1) res = res / n * (n - 1);
  return res;
}
int solve(int l, int r, int d) {
  if (phi[d] == 1) return 1;
  if (l == r) return w[l] < phi[d] ? w[l] : w[l] % phi[d] + phi[d];
  return ksm(w[l], solve(l + 1, r, d + 1), phi[d]);
}
int main() {
  scanf("%d%d", &n, &m);
  phi[tot++] = m;
  while (m != 1) {
    phi[tot++] = Phi(m);
    m = phi[tot - 1];
  }
  for (int i = 1; i <= n; ++i) scanf("%d", &w[i]);
  scanf("%d", &q);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    printf("%d\n", solve(l, r, 0) % phi[0]);
  }
  return 0;
}