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 long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while ('0' > ch || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = (x << 1) + (x << 3) + ch - '0';
    ch = getchar();
  }
  return x * f;
}
long long pre[4000005], cnt, book[4000005], phi[4000005], mod, M, m, n,
    w[4000005], q;
struct node {
  long long x, y;
} b[4000005];
unordered_map<long long, long long> Q;
void shai() {
  phi[1] = 1;
  for (int i = 2; i <= 4000000; i++) {
    if (!book[i]) {
      book[i] = i;
      pre[++cnt] = i;
      phi[i] = i - 1;
    }
    for (int j = 1; j <= cnt; j++) {
      if (book[i] < pre[j] || pre[j] * i > 4000000) break;
      book[i * pre[j]] = pre[j];
      if (i % pre[j] == 0)
        phi[i * pre[j]] = phi[i] * pre[j];
      else
        phi[i * pre[j]] = phi[i] * (pre[j] - 1);
    }
  }
  for (int i = 2; i <= 4000000; i++) phi[i] = phi[i - 1] + phi[i];
}
long long find(long long x) {
  if (x <= 4000000) return phi[x];
  if (Q[x]) return Q[x];
  long long ans = 0;
  for (long long l = 2, r; l <= x; l = r + 1) {
    r = x / (x / l);
    ans = ans + find(x / l) * (r - l + 1);
  }
  Q[x] = (x + 1) * x / 2 - ans;
  return Q[x];
}
long long ksm1(long long x, long long y, long long mod) {
  long long res = 1;
  while (y) {
    if (y & 1) res = (res * x) % mod;
    x = (x * x) % mod;
    y >>= 1;
  }
  return res % mod;
}
long long ksm(long long x, long long y, long long mod) {
  long long res = 1, zlk = 0, wyx = 0;
  while (y) {
    if (y & 1) {
      if (!zlk && (res * x >= mod || wyx)) zlk = 1;
      res = (x * res) % mod;
    }
    if (x * x >= mod) wyx = 1;
    x = (x * x) % mod;
    y >>= 1;
  }
  return res + zlk * mod;
}
long long work(long long x, long long y, long long mod) {
  if (mod == 1) return 1ll;
  if (x > y) return 1ll;
  long long s = work(x + 1, y, find(mod) - find(mod - 1));
  if (mod == m)
    return ksm1(w[x], s, mod);
  else
    return ksm(w[x], s, mod);
}
int main() {
  shai();
  n = read();
  m = read();
  M = find(m);
  for (int i = 1; i <= n; i++) w[i] = read();
  q = read();
  for (int i = 1; i <= q; i++) {
    b[i].x = read(), b[i].y = read();
    printf("%lld\n", work(b[i].x, b[i].y, m) % m);
  }
  return 0;
}