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

<image>

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 maxn = 1e5 + 5;
bool vis;
int add(int x, int y, int mod) {
  x += y;
  if (x >= mod) x -= mod;
  return x;
}
int mul(int x, int y, int mod) {
  long long z = 1LL * x * y;
  if (z >= mod) vis = 1;
  return z - z / mod * mod;
}
int powt(int a, int b, int mod) {
  int r = 1;
  while (b) {
    if (b & 1) r = mul(r, a, mod);
    a = mul(a, a, mod);
    b >>= 1;
  }
  return r;
}
int eular(int k) {
  int i, s;
  s = k;
  for (i = 2; i * i <= k; i++) {
    if (k % i == 0) s = s / i * (i - 1);
    while (k % i == 0) k /= i;
  }
  if (k > 1) s = s / k * (k - 1);
  return s;
}
int a[maxn];
unordered_map<int, int> q;
int solve(int l, int r, int m) {
  if (m == 1) {
    vis = 1;
    return 0;
  }
  if (l == r) {
    vis = a[l] >= m;
    return a[l] % m;
  }
  if (q.find(m) == q.end()) q[m] = eular(m);
  int mm = q[m];
  int d = solve(l + 1, r, mm);
  if (a[l] == 1) vis = 0;
  if (vis)
    return powt(a[l], d + mm, m);
  else
    return powt(a[l], d, m);
}
int main() {
  int n, m, q, i, l, r;
  scanf("%d%d", &n, &m);
  for (i = 1; i <= n; i++) scanf("%d", &a[i]);
  scanf("%d", &q);
  while (q--) {
    scanf("%d%d", &l, &r);
    vis = 0;
    printf("%d\n", solve(l, r, m));
  }
  return 0;
}