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

<image>

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 inf = 1 << 30;
const long long INF = 1LL << 60;
const int MaxN = 100000;
long long n, Q, Pt;
map<long long, long long> phi;
long long a[MaxN + 5];
inline long long Mod(long long x, long long y) {
  return (x < y ? x : x % y + y);
}
long long qwr(long long x, long long y, long long mod) {
  long long res = 1LL;
  while (y > 0) {
    if (y & 1) res = Mod(res * x, mod);
    x = Mod(x * x, mod);
    y = y >> 1;
  }
  return res;
}
long long Get_phi(long long n) {
  if (phi[n]) return phi[n];
  long long t = (long long)sqrt(1.0 * n + 0.5);
  long long res = n, x = n;
  for (int i = 2; i <= t; i++) {
    if (n % i == 0) {
      res = res / i * (i - 1);
      while (n % i == 0) n /= i;
    }
  }
  if (n > 1) res = res / n * (n - 1);
  phi[x] = res;
  return res;
}
long long Solve(int l, int r, long long mod) {
  if (l == r || mod == 1) return Mod(a[l], mod);
  long long ans = Solve(l + 1, r, Get_phi(mod));
  return qwr(a[l], ans, mod);
}
int main() {
  while (scanf("%lld %lld", &n, &Pt) != EOF) {
    for (int i = 1; i <= n; i++) scanf("%lld", &a[i]);
    scanf("%d", &Q);
    while (Q--) {
      int l, r;
      scanf("%d %d", &l, &r);
      printf("%lld\n", Solve(l, r, Pt) % Pt);
    }
  }
  return 0;
}