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>
const int N = 100010;
const int M = 100;
const long long INF = 1e15;
int w[N], phi[M];
long long update(int w, long long exp) {
  if (w == 1) {
    return 1;
  }
  if (exp >= 50) {
    return INF;
  }
  return (long long)std::min((double)INF, pow(w, exp));
}
int getphi(int m) {
  int ret = 1;
  for (int i = 2; i * i <= m; ++i) {
    if (m % i == 0) {
      while (m % i == 0) {
        ret *= i;
        m /= i;
      }
      ret = ret / i * (i - 1);
    }
  }
  if (m > 1) {
    ret *= m - 1;
  }
  return ret;
}
int powermod(int a, int exp, int moder) {
  int ret = 1;
  for (; exp > 0; exp >>= 1) {
    if (exp & 1) {
      ret = 1ll * ret * a % moder;
    }
    a = 1ll * a * a % moder;
  }
  return ret % moder;
}
int main() {
  int n, m;
  scanf("%d%d", &n, &m);
  int mm = m;
  std::set<int> one;
  for (int i = 0; i < n; ++i) {
    scanf("%d", &w[i]);
    if (w[i] == 1) {
      one.insert(w[i]);
    }
  }
  int cnt = 0;
  phi[cnt++] = m;
  while (m > 1) {
    phi[cnt++] = m = getphi(m);
  }
  m = mm;
  int q;
  scanf("%d", &q);
  while (q--) {
    int l, r;
    scanf("%d%d", &l, &r);
    --l, --r;
    if (l == r) {
      printf("%d\n", w[l] % m);
      continue;
    }
    auto u = one.upper_bound(std::min(l + cnt - 1, r));
    int lastone = u == one.end() ? n : *u;
    lastone = std::min(lastone, r + 1);
    if (r - l + 1 > cnt) {
      r = l + cnt - 1;
    }
    long long appr = 0;
    if (lastone - r >= 10) {
      appr = INF;
    } else {
      appr = 1;
      for (int i = lastone - 1; i > r; --i) {
        appr = update(w[i], appr);
      }
    }
    int pre = 1;
    for (int i = r; i >= l; --i) {
      int exp = appr >= phi[i + 1 - l] ? pre + phi[i + 1 - l] : pre;
      pre = powermod(w[i], exp, phi[i - l]);
      appr = update(w[i], appr);
    }
    printf("%d\n", pre % m);
  }
  return 0;
}