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 = 100010;
int mul_mod(int a, int b, int p) {
  return (long long)a * b >= p ? (long long)a * b % p + p : a * b;
}
int power_mod(int a, int n, int p) {
  int ret = 1;
  while (n) {
    if (n & 1) ret = mul_mod(ret, a, p);
    a = mul_mod(a, a, p);
    n >>= 1;
  }
  return ret;
}
map<int, int> phi;
int euler(int n) {
  if (phi.count(n)) return phi[n];
  int ret = n;
  for (int x = 2; x * x <= n; x++) {
    if (n % x == 0) {
      ret = ret / x * (x - 1);
      while (n % x == 0) n /= x;
    }
  }
  if (n > 1) ret = ret / n * (n - 1);
  return phi[n] = ret;
}
int w[MAXN];
int calc(int l, int r, int p) {
  if (p == 1 || l == r) return power_mod(w[l], 1, p);
  int e = calc(l + 1, r, euler(p));
  return power_mod(w[l], e, p);
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) scanf("%d", &w[i]);
  int q;
  scanf("%d", &q);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    printf("%d\n", calc(l, r, m) % m);
  }
  return 0;
}