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;
int n, m;
const int maxn = 1e5 + 10;
long long w[maxn];
inline long long Mod(long long a, long long b) { return a < b ? a : a % b + b; }
long long qpow(long long a, int b, const int mod) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) res = Mod(res * a, mod);
    a = Mod(a * a, mod);
    b >>= 1;
  }
  return res;
}
long long eulr(long long n) {
  long long ans = n;
  long long tmp = n;
  for (long long i = 2; i * i <= tmp; i++) {
    if (n % i == 0) {
      ans = ans / i * (i - 1);
      while (n % i == 0) {
        n /= i;
      }
    }
  }
  if (n > 1) {
    ans = ans / n * (n - 1);
  }
  return ans;
}
unordered_map<long long, long long> mp;
long long cal_eulr(long long n) {
  if (mp.count(n)) {
    return mp[n];
  }
  long long tmp = eulr(n);
  mp[n] = tmp;
  return tmp;
}
long long solve(int l, int r, int m) {
  if (l == r) return Mod(w[l], m);
  if (m == 1) return Mod(w[l], m);
  return qpow(w[l], solve(l + 1, r, cal_eulr(m)), m);
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++) {
    scanf("%lld", &w[i]);
  }
  int q;
  int l, r;
  scanf("%d", &q);
  while (q--) {
    scanf("%d%d", &l, &r);
    printf("%lld\n", solve(l, r, m) % m);
  }
  return 0;
}