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;
inline int read() {
  int out = 0, fh = 1;
  char jp = getchar();
  while ((jp > '9' || jp < '0') && jp != '-') jp = getchar();
  if (jp == '-') fh = -1, jp = getchar();
  while (jp >= '0' && jp <= '9') out = out * 10 + jp - '0', jp = getchar();
  return out * fh;
}
void print(int x) {
  if (x >= 10) print(x / 10);
  putchar('0' + x % 10);
}
void write(int x, char c) {
  if (x < 0) putchar('-'), x = -x;
  print(x);
  putchar(c);
}
int phi(int x) {
  int res = x;
  for (int i = 2; i * i <= x; ++i)
    if (x % i == 0) {
      res /= i, res *= i - 1;
      while (x % i == 0) x /= i;
    }
  if (x > 1) res /= x, res *= x - 1;
  return res;
}
int mul(int a, int b, int Mod) {
  long long pr = 1LL * a * b;
  if (pr < Mod) return pr;
  return pr % Mod + Mod;
}
int fpow(int a, int b, int Mod) {
  int res = 1;
  while (b) {
    if (b & 1) res = mul(res, a, Mod);
    a = mul(a, a, Mod);
    b >>= 1;
  }
  return res;
}
int f(int x, int Mod) {
  if (x < Mod) return x;
  return x % Mod + Mod;
}
const int N = 1e5 + 10;
int n, m, q, Mod[N], k = 0, a[N];
int query(int l, int r, int p) {
  if (l == r || p == k) return f(a[l], Mod[p]);
  int base = a[l], expo = query(l + 1, r, p + 1);
  return fpow(base, expo, Mod[p]);
}
signed main() {
  n = read(), m = read();
  while (1) {
    Mod[++k] = m;
    if (m == 1) break;
    m = phi(m);
  }
  for (int i = 1; i <= n; ++i) a[i] = read();
  q = read();
  for (int i = 1; i <= q; ++i) {
    int l = read(), r = read();
    int ans = query(l, r, 1) % Mod[1];
    write(ans, '\n');
  }
  return 0;
}