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>
inline long long read() {
  register long long x = 0;
  register int y = 1;
  register char c = std::getchar();
  while (c < '0' || c > '9') {
    if (c == '-') y = 0;
    c = std::getchar();
  }
  while (c >= '0' && c <= '9') {
    x = x * 10 + (c ^ 48);
    c = std::getchar();
  }
  return y ? x : -x;
}
int w[100006];
std::map<long long, long long> map;
inline long long get_phi(long long n) {
  if (map.find(n) != map.end()) return map[n];
  long long ret = n;
  for (register long long i = 2; i * i <= n; i++) {
    if (!(n % i)) ret = ret / i * (i - 1);
    while (!(n % i)) n /= i;
  }
  if (n > 1) ret = ret / n * (n - 1);
  map[n] = ret;
  return ret;
}
inline long long mo(long long x, long long mod) {
  return x < mod ? x : (x % mod + mod);
}
inline long long power(long long a, long long b, long long mod) {
  long long ret = 1;
  while (b) {
    if (b & 1) ret = mo(ret * a, mod);
    a = mo(a * a, mod);
    b >>= 1;
  }
  return ret;
}
long long work(int l, int r, long long p) {
  if (l == r || p == 1) return mo(w[l], p);
  return power(w[l], work(l + 1, r, get_phi(p)), p);
}
int main() {
  long long n = read(), p = read();
  for (register int i = 1; i <= n; i++) w[i] = read();
  int q = read();
  while (q--) {
    int l = read(), r = read();
    std::printf("%lld\n", work(l, r, p) % p);
  }
  return 0;
}