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>
#pragma warning(disable : 4996)
using namespace std;
const int maxn = 1e8 + 5;
using namespace std;
int sequence[100050];
map<long long, long long> phi;
long long euler(long long n) {
  int ret = n;
  if (phi[ret]) return phi[ret];
  for (int i = 2; i <= sqrt(n + 0.5); i++) {
    if (n % i == 0) {
      ret = ret / i * (i - 1);
      while (n % i == 0) {
        n /= i;
      }
    }
  }
  if (n > 1) ret = ret / n * (n - 1);
  phi[n] = ret;
  return ret;
}
long long qpow(long long x, long long y, long long mod) {
  long long ret = 1;
  while (y) {
    if (y & 1) ret = ret * x < mod ? ret * x : ret * x % mod + mod;
    x = x * x < mod ? x * x : x * x % mod + mod;
    y >>= 1;
  }
  return ret;
}
long long Solve(long long a, long long b, long long mod) {
  if (mod == 1 || b == a)
    return sequence[a] < mod ? sequence[a] : sequence[a] % mod + mod;
  return qpow(sequence[a], Solve(a + 1, b, euler(mod)), mod);
}
int main() {
  int len, m, s;
  scanf("%d %d", &len, &m);
  for (int i = 1; i <= len; i++) scanf("%d", &sequence[i]);
  int qn;
  scanf("%d", &qn);
  long long l, r, ans;
  while (qn--) {
    scanf("%lld %lld", &l, &r);
    ans = Solve(l, r, m) % m;
    printf("%lld\n", ans);
  }
  return 0;
}