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 MAXN = (int)1e5 + 5;
vector<int> vec;
int arr[MAXN];
int n, m, q;
int mod(long long x, int m) {
  if (x <= 32) {
    return x;
  } else {
    return 32 + (x - 32) % m;
  }
}
int mulMod(int a, int b, int m) { return mod(a * 1ll * b, m); }
int binPow(int a, int b, int m) {
  int ret = 1;
  while (b > 0) {
    if (b & 1) {
      ret = mulMod(ret, a, m);
    }
    a = mulMod(a, a, m);
    b >>= 1;
  }
  return ret;
}
int phi(int x) {
  int ret = x;
  for (int i = 2; i * i <= x; ++i) {
    if (x % i == 0) {
      ret -= ret / i;
      x /= i;
      while (x % i == 0) {
        x /= i;
      }
    }
  }
  if (x > 1) {
    ret -= ret / x;
  }
  return ret;
}
int calc(int l, int r, int p) {
  if (p == vec.size() - 1) {
    return 1;
  }
  if (l == r) {
    return mod(arr[l], vec[p]);
  }
  int x = calc(l + 1, r, p + 1);
  return binPow(arr[l], x, vec[p]);
}
void solve() {
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", &arr[i]);
  }
  scanf("%d", &q);
  vec.push_back(m);
  while (vec.back() != 1) {
    int x = vec.back();
    vec.push_back(phi(x));
  }
  for (int i = 1; i <= q; ++i) {
    int l, r;
    scanf("%d %d", &l, &r);
    printf("%d\n", calc(l, r, 0) % m);
  }
}
int main() {
  int tt = 1;
  while (tt--) {
    solve();
  }
  return 0;
}