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>
#pragma GCC optimize(2)
using namespace std;
template <class T>
void rd(T &x) {
  x = 0;
  char c = getchar();
  long long f = 1;
  while (!isdigit(c)) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (isdigit(c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getchar();
  x *= f;
}
template <class T>
void pt(T x) {
  if (x < 0) putchar('-'), x = (~x) + 1;
  if (x > 9) pt(x / 10);
  putchar((x % 10) ^ 48);
}
template <class T>
T Min(T x, T y) {
  return x < y ? x : y;
}
template <class T>
T Max(T x, T y) {
  return x > y ? x : y;
}
const int N = 1e5 + 5;
map<int, int> Map;
int n, mod, q, l, r, a[N];
int Mod(long long x, int p) { return x < p ? x : x % p + p; }
int qkpow(int a, int b, int mod) {
  int res = 1;
  while (b) {
    if (b & 1) res = Mod(1ll * res * a, mod);
    b >>= 1;
    a = Mod(1ll * a * a, mod);
  }
  return res;
}
int phi(int n) {
  if (Map.count(n)) return Map[n];
  int res = n, pos = n;
  for (int i = 2; i * i <= n; i++)
    if (n % i == 0) {
      res = res / i * (i - 1);
      while (n % i == 0) n /= i;
    }
  if (n > 1) res = res / n * (n - 1);
  return Map[pos] = res;
}
int solve(int l, int r, int mod) {
  if (l == r || mod == 1) return Mod(a[l], mod);
  return qkpow(a[l], solve(l + 1, r, phi(mod)), mod);
}
int main() {
  rd(n), rd(mod);
  for (int i = 1; i <= n; i++) rd(a[i]);
  rd(q);
  while (q--) {
    rd(l), rd(r);
    pt(solve(l, r, mod) % mod);
    puts("");
  }
  return 0;
}