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;
int a[100005], mod[100005];
int n, p;
bool fg;
inline int read() {
  int n = 0, f = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    n = n * 10 + c - '0';
    c = getchar();
  }
  return n * f;
}
inline int pro(long long x, int md) { return x < md ? x : x % md + md; }
inline int mi(int x, int y, int md) {
  register int z = 1;
  for (; y; x = pro(1LL * x * x, md), y >>= 1)
    if (y & 1) z = pro(1LL * z * x, md);
  return z;
}
int dfs(int x, int y, int lim) {
  if (x == lim || mod[y] == 1)
    return a[x] >= mod[y] ? a[x] % mod[y] + mod[y] : a[x];
  return mi(a[x], dfs(x + 1, y + 1, lim), mod[y]);
}
int main() {
  register int i, j, x, y;
  n = read();
  mod[1] = read();
  for (i = 1; mod[i] > 1; ++i) {
    mod[i + 1] = x = mod[i];
    for (j = 2; j * j <= x; ++j) {
      for (fg = 0; x % j == 0; x /= j, fg = true)
        ;
      if (fg) mod[i + 1] = 1LL * mod[i + 1] * (j - 1) / j;
    }
    if (x > 1) mod[i + 1] = 1LL * mod[i + 1] * (x - 1) / x;
  }
  for (i = 1; i <= n; ++i) a[i] = read();
  for (p = read(); p; --p) {
    x = read();
    y = read();
    printf("%d\n", dfs(x, 1, y) % mod[1]);
  }
}