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 int n, m;
vector<long long int> phi, v;
void createphi(long long int a) {
  long long int res = a, x = a;
  for (long long int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      res = res * (i - 1) / i;
      while (x % i == 0) x /= i;
    }
  }
  if (x > 1) res = res * (x - 1) / x;
  phi.push_back(res);
  if (res == 1) return;
  createphi(res);
  return;
}
long long int amodb(long long int a, long long int b) {
  if (a < b) return a;
  long long int temp = a / b;
  temp = a - temp * b;
  temp += b;
  return temp;
}
long long int bigmod(long long int a, long long int pw, long long int mod) {
  if (pw == 0) return 1;
  long long int x = bigmod(a, pw / 2, mod);
  x = amodb(x * x, mod);
  if (pw % 2) x = amodb(x * a, mod);
  return x;
}
long long int rec(long long int st, long long int ed, long long int md) {
  if (st == ed) {
    return amodb(v[st], phi[md]);
  }
  if (phi[md] == 1) return 1LL;
  return bigmod(v[st], rec(st + 1, ed, md + 1), phi[md]);
}
int main() {
  cin >> n >> m;
  for (int i = 0; i < n; i++) {
    long long int a;
    cin >> a;
    v.push_back(a);
  }
  phi.push_back(m);
  createphi(m);
  long long int q;
  cin >> q;
  while (q--) {
    long long int l, r;
    cin >> l >> r;
    cout << rec(l - 1, r - 1, 0LL) % m << "\n";
  }
  return 0;
}