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;
namespace IO {
const int __buffsize = 1000000;
char __buff[__buffsize];
char *__buffS, *__buffT;
char getch() {
  if (__buffS == __buffT) {
    __buffT = (__buffS = __buff) + fread(__buff, 1, __buffsize, stdin);
    if (__buffS == __buffT) return EOF;
  }
  return *__buffS++;
}
int read() {
  int T = 0, f = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-') c = getchar();
  if (c == '-') f = -1, c = getchar();
  while (c >= '0' && c <= '9') {
    T = ((T << 1) + (T << 3)) + c - 48;
    c = getchar();
  }
  return T * f;
}
void write(int x) {
  if (x < 0) putchar('0'), x = -x;
  if (x >= 10) write(x / 10);
  putchar((x % 10) + '0');
}
void writeln(int x) {
  write(x);
  puts("");
}
};  // namespace IO
using namespace IO;
int n;
const int maxn = 800010;
long long a[maxn], p[maxn];
int Pow(int, int, int);
int solve(int l, int r, int Mod, int deep) {
  if (Mod == 1) return 1;
  long long now = a[l] % Mod;
  if (!now) return 0;
  if (l == r) return now;
  int nxt = min(l + 5, r);
  for (int i = l + 1; i < nxt; i++)
    if (a[i] == 1) {
      nxt = r = i;
      break;
    }
  long long last = a[nxt], x;
  if (last >= p[deep])
    return Pow(now, solve(l + 1, r, p[deep], deep + 1) + p[deep], Mod);
  for (int i = nxt - 1; i > l; i--) {
    long long mi = last;
    last = 1;
    x = a[i];
    for (int j = 1; j <= mi; j++) {
      last = last * x;
      if (last >= p[deep])
        return Pow(now, solve(l + 1, r, p[deep], deep + 1) + p[deep], Mod);
    }
  }
  return Pow(now, solve(l + 1, r, p[deep], deep + 1), Mod);
}
int Pow(int a, int b, int Mod) {
  int Ans = 1;
  for (; b; b >>= 1, a = 1LL * a * a % Mod)
    if (b & 1) Ans = 1LL * Ans * a % Mod;
  return Ans;
}
int Getphi(int x) {
  int ans = x;
  for (int i = 2; i * i <= x; i++) {
    if (x % i == 0) {
      ans = ans / i * (i - 1);
      while (x % i == 0) x /= i;
    }
  }
  if (x > 1) ans = ans / x * (x - 1);
  return ans;
}
int Mod, cnt;
void init() {
  scanf("%d%d", &n, &Mod);
  for (int i = 1; i <= n; i++) scanf("%I64d", &a[i]);
  cnt = 0;
  p[0] = Mod;
  while (p[cnt] != 1) p[++cnt] = Getphi(p[cnt - 1]);
  p[++cnt] = 1;
}
int main() {
  init();
  int m = read();
  while (m--) {
    int x = read(), y = read();
    printf("%d\n", solve(x, y, Mod, 1) % Mod);
  }
}