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 = 100100;
int n, q;
long long int m;
vector<long long int> mods;
long long int w[N];
long long int phi(long long int x) {
  long long int ans = x;
  for (long long int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      ans -= ans / i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    ans -= ans / x;
  }
  return ans;
}
long long int magic(long long int x, long long int mod) {
  if (x < 32) {
    return x;
  }
  return 32 + (x - 32) % mod;
}
long long int fexp(long long int base, long long int e, long long int mod) {
  long long int ans = 1;
  while (e > 0) {
    if (e & 1) {
      ans = magic(ans * base, mod);
    }
    base = magic(base * base, mod);
    e >>= 1;
  }
  return ans;
}
long long int go(int l, int r, int on) {
  if (r == l) {
    return magic(w[l], mods[on]);
  }
  if (mods[on] == 1) {
    return 53;
  }
  long long int e = go(l + 1, r, on + 1);
  return fexp(w[l], e, mods[on]);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  cin >> n >> m;
  mods.push_back(m);
  while (mods.back() != 1) {
    mods.push_back(phi(mods.back()));
  }
  for (int i = 0; i < n; i++) {
    cin >> w[i];
  }
  cin >> q;
  while (q--) {
    int l, r;
    cin >> l >> r;
    l--;
    r--;
    cout << go(l, r, 0) % mods[0] << endl;
  }
  return 0;
}