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;
long long v[100001];
long long mod[101];
long long euler(long long nr) {
  long long rez = nr;
  long long p = 0;
  long long d = 2;
  while ((nr & 1) == 0) {
    nr >>= 1;
    p++;
  }
  if (p != 0) {
    rez /= d;
    rez *= (d - 1);
  }
  d = 3;
  while (d * d <= nr) {
    p = 0;
    while (nr % d == 0) {
      nr /= d;
      p++;
    }
    if (p != 0) {
      rez /= d;
      rez *= (d - 1);
    }
    d += 2;
  }
  if (nr > 1) {
    rez /= nr;
    rez *= (nr - 1);
  }
  return rez;
}
long long putere(long long a, long long b, long long MOD) {
  long long ca = a;
  long long rez = 1;
  long long i;
  for (i = 0; (1LL << i) <= b; i++) {
    if (((1LL << i) & b) != 0) {
      if (rez * ca >= MOD)
        rez = rez * ca % MOD + MOD;
      else
        rez *= ca;
    }
    if (ca * ca >= MOD)
      ca = ca * ca % MOD + MOD;
    else
      ca *= ca;
  }
  return (int)rez;
}
long long getRez(long long st, long long dr, long long m) {
  if (mod[m] == 1) return 1;
  if (st == dr) {
    if (v[st] < mod[m]) return v[st];
    return v[st] % mod[m] + mod[m];
  }
  return putere(v[st], getRez(st + 1, dr, m + 1), mod[m]);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n;
  long long MOD;
  cin >> n >> MOD;
  mod[1] = MOD;
  long long i = 2;
  while (mod[i - 1] != 1) {
    mod[i] = euler(mod[i - 1]);
    i++;
  }
  for (i = 1; i <= n; i++) cin >> v[i];
  long long t;
  cin >> t;
  while (t > 0) {
    long long st, dr;
    cin >> st >> dr;
    cout << getRez(st, dr, 1) % mod[1] << "\n";
    t--;
  }
  return 0;
}