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 = 1e5 + 5;
int val[N], mo[N], tl, is;
inline long long qpow(long long x, int y, int mod) {
  long long ret = 1;
  while (y) {
    if (y & 1) {
      ret *= x;
      if (ret >= mod) is = 1, ret = ret % mod + mod;
    }
    x *= x;
    if (x >= mod) is = 1, x = x % mod + mod;
    y >>= 1;
  }
  return ret;
}
int calc(int l, int r, int pos) {
  if (mo[pos] == 1) return 1;
  if (l == r) {
    if (val[l] >= mo[pos]) return val[l] % mo[pos] + mo[pos];
    return val[l];
  }
  return qpow(val[l], calc(l + 1, r, pos + 1), mo[pos]);
}
int main() {
  int n, p, q, i;
  scanf("%d%d", &n, &p);
  for (i = 1; i <= n; i++) scanf("%d", &val[i]);
  mo[++tl] = p;
  while (p != 1) {
    int tmp = p, phi = p;
    for (i = 2; i * i <= p; i++) {
      if (tmp == 1) break;
      if (!(tmp % i)) {
        phi = phi / i * (i - 1);
        while (!(tmp % i)) tmp /= i;
      }
    }
    if (tmp != 1) phi = phi / tmp * (tmp - 1);
    mo[++tl] = phi;
    p = phi;
  }
  scanf("%d", &q);
  for (i = 1; i <= q; i++) {
    int l, r;
    scanf("%d%d", &l, &r);
    is = 0;
    printf("%d\n", calc(l, r, 1) % mo[1]);
  }
  return 0;
}