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;
#pragma warning(disable : 4996)
long long n, MOD;
long long w[100005];
long long q, l, r;
long long ph[100005];
long long LL;
long long qpow(long long x, long long y, long long MOD) {
  long long ret = 1;
  int flag = 0;
  while (y) {
    if (y & 1) {
      ret = ret * x;
      if (ret >= MOD) {
        ret = ret % MOD;
        flag = 1;
      }
    }
    x = x * x;
    if (x >= MOD) x = x % MOD + MOD;
    y >>= 1;
  }
  if (flag) ret += MOD;
  return ret;
}
long long Euler(long long n) {
  long long ret = n;
  for (long long i = 2; i * i <= n; i++) {
    if (n % i == 0) ret = ret / i * (i - 1);
    while (n % i == 0) n /= i;
  }
  if (n > 1) ret = ret / n * (n - 1);
  return ret % MOD;
}
long long solve(long long l, long long r, long long MOD) {
  if (l == r) {
    if (w[r] >= MOD)
      return w[r] % MOD + MOD;
    else
      return w[r];
  }
  if (MOD == 1) return 1;
  return qpow(w[l], solve(l + 1, r, ph[l - LL + 2]), ph[l - LL + 1]);
}
int main() {
  scanf("%lld%lld", &n, &MOD);
  ph[1] = MOD;
  scanf("%lld", &w[1]);
  for (int i = 2; i <= n; i++) {
    scanf("%lld", &w[i]);
    ph[i] = Euler(ph[i - 1]);
  }
  scanf("%lld", &q);
  while (q--) {
    scanf("%lld%lld", &l, &r);
    if (l == r) {
      printf("%lld\n", w[l] % MOD);
      continue;
    }
    LL = l;
    printf("%lld\n", solve(l, r, ph[1]) % MOD);
  }
  return 0;
}