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;
using std::bitset;
const double Pi = acos(-1);
inline long long read() {
  long long x = 0;
  bool fu = 0;
  char ch = 0;
  while (ch > '9' || ch < '0') {
    ch = getchar();
    if (ch == '-') fu = 1;
  }
  while (ch <= '9' && ch >= '0') x = (x * 10 - 48 + ch), ch = getchar();
  return fu ? -x : x;
}
long long n, mod, w[100002], q, l, r;
map<long long, long long> phi;
inline long long go(long long num) {
  long long rt = num;
  for (long long i = 2; i * i <= num; i++) {
    if (num % i == 0) rt = rt * (i - 1) / i;
    while (num % i == 0) num /= i;
  }
  if (num > 1) rt = rt * (num - 1) / num;
  return rt;
}
inline long long pw(long long x, long long p, long long mod) {
  bool flag = 0;
  long long rt = 1;
  while (p) {
    if (p & 1) {
      if (rt * x >= mod) flag = 1;
      rt = rt * x % mod;
    }
    if (x * x >= mod) flag = 1;
    x = x * x % mod, p >>= 1;
  }
  return rt + flag * mod;
}
inline long long dfs(long long pos, long long mod) {
  if (pos > r || mod == 1) return 1;
  return pw(w[pos], dfs(pos + 1, phi[mod]), mod);
}
signed main() {
  cin >> n >> mod;
  l = mod;
  phi[1] = 1;
  while (l > 1) phi[l] = go(l), l = phi[l];
  for (register long long i = 1, iend = n; i <= iend; ++i) w[i] = read();
  cin >> q;
  while (q--) {
    l = read(), r = read();
    cout << dfs(l, mod) % mod << '\n';
  }
  return 0;
}