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 = 1e5 + 5;
long long n, mod, a[N], q;
long long qpow(long long a, long long b, long long m) {
  long long res = 1;
  while (b) {
    if (b & 1) res = (res * a >= m ? res * a % m + m : res * a);
    a = a * a >= m ? a * a % m + m : a * a;
    b >>= 1;
  }
  return res;
}
map<long long, long long> mp;
long long myphi(long long n) {
  if (mp.count(n)) return mp[n];
  long long ans = n;
  long long num = n;
  for (int i = 2; i * i <= n; ++i) {
    if (n % i == 0) {
      ans -= ans / i;
      while (n % i == 0) n /= i;
    }
  }
  if (n > 1) ans -= ans / n;
  mp[num] = ans;
  return ans;
}
long long solve(long long l, long long r, long long mod) {
  if (l == r || mod == 1) return (a[l] < mod) ? a[l] : (a[l] % mod + mod);
  return qpow(a[l], solve(l + 1, r, myphi(mod)), mod);
}
int main() {
  scanf("%lld%lld", &n, &mod);
  for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]);
  scanf("%lld", &q);
  while (q--) {
    int L, R;
    scanf("%d%d", &L, &R);
    printf("%lld\n", solve(L, R, mod) % mod);
  }
  return 0;
}