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 N = 1e5 + 5;
int n, m, w[N], p[N], tot;
char nchar() {
  static const int S = 1e7;
  static char s[S], *h = s + S, *t = h;
  if (h == t) fread(s, 1, S, stdin), h = s;
  return *h++;
}
int rd() {
  char c;
  do {
    c = nchar();
  } while (!isdigit(c));
  int x = 0;
  do {
    x = x * 10 + c - '0', c = nchar();
  } while (isdigit(c));
  return x;
}
int PHI(int n) {
  int m = n;
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) {
      m = m / i * (i - 1);
      while (n % i == 0) n /= i;
    }
  if (n > 1) m = m / n * (n - 1);
  return m;
}
int mod(long long x, int P) { return x < P ? x : x % P + P; }
int Pow(int x, int t, int P) {
  int m = 1;
  for (; t; t >>= 1, x = mod(1LL * x * x, P))
    if (t & 1) m = mod(1LL * m * x, P);
  return m;
}
int CC(int l, int r, int c) {
  if (l == r || c == tot) return mod(w[l], p[c]);
  int t = CC(l + 1, r, c + 1);
  return Pow(w[l], t, p[c]);
}
int main() {
  n = rd(), m = rd();
  for (int i = (1), _ = (n); i <= _; i++) w[i] = rd();
  p[++tot] = m;
  while (p[tot] > 1) p[tot + 1] = PHI(p[tot]), tot++;
  for (int OP = (1), _ = (rd()); OP <= _; OP++) {
    int l = rd(), r = rd();
    printf("%d\n", CC(l, r, 1) % p[1]);
  }
  return 0;
}