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 INF = 0x3f3f3f3f;
const int MOD = 1000000007;
const int MXN = 1e6 + 6;
int n, mod;
long long ar[MXN];
unordered_map<int, int> mp;
int get_phi(int n) {
  if (mp.count(n)) return mp[n];
  int ans = n, tmp = sqrt(n), tn = n;
  for (int i = 2; i <= tmp; ++i) {
    if (n % i == 0) {
      while (n % i == 0) n /= i;
      ans = ans / i * (i - 1);
    }
    if (n == 1) break;
  }
  if (n > 1) ans = ans / n * (n - 1);
  mp[tn] = ans;
  return ans;
}
long long ksm(long long a, long long b, int mod) {
  long long res = 1;
  for (; b; b >>= 1, a = a * a < mod ? a * a : a * a % mod + mod) {
    if (b & 1) res = a * res < mod ? a * res : a * res % mod + mod;
  }
  return res;
}
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long solve(int l, int r, int mod) {
  if (l == r || mod == 1) return ar[l] < mod ? ar[l] : ar[l] % mod + mod;
  return ksm(ar[l], solve(l + 1, r, get_phi(mod)), mod);
}
int main() {
  mp[1] = 1;
  mp[2] = 1;
  scanf("%d%d", &n, &mod);
  for (int i = 1; i <= n; ++i) scanf("%lld", &ar[i]);
  int q, l, r;
  scanf("%d", &q);
  while (q--) {
    scanf("%d%d", &l, &r);
    printf("%lld\n", solve(l, r, mod) % mod);
  }
  return 0;
}