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 L = (1 << 21) + 1;
char ibuf[L], *iS, *iT, obuf[L], *oS = obuf, *oT = obuf + L - 1, c, st[55];
int f, tp;
inline void flush() {
  fwrite(obuf, 1, oS - obuf, stdout);
  oS = obuf;
}
inline void putc(char x) {
  *oS++ = x;
  if (oS == oT) flush();
}
template <class I>
inline void gi(I& x) {
  for (f = 1, c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, L, stdin),
                              (iS == iT ? EOF : *iS++))
                            : *iS++);
       c < '0' || c > '9';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, L, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    if (c == '-') f = -1;
  for (x = 0; c <= '9' && c >= '0';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, L, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    x = x * 10 + (c & 15);
  x *= f;
}
template <class I>
inline void print(I x) {
  if (!x) putc('0');
  if (x < 0) putc('-'), x = -x;
  while (x) st[++tp] = x % 10 + '0', x /= 10;
  while (tp) putc(st[tp--]);
}
inline void gs(char* s, int& l) {
  for (c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, L, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++);
       c < 'a' || c > 'z';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, L, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    ;
  for (l = 0; c <= 'z' && c >= 'a';
       c = (iS == iT ? (iT = (iS = ibuf) + fread(ibuf, 1, L, stdin),
                       (iS == iT ? EOF : *iS++))
                     : *iS++))
    s[l++] = c;
}
};  // namespace io
using io::gi;
using io::gs;
using io::print;
using io::putc;
const int N = 100005, G = 65;
int n, num[N], p, mod[G], m, q, ans;
int phi(int n) {
  int ret = n;
  for (int p = 2; p * p <= n; p++)
    if (n % p == 0) {
      ret = ret / p * (p - 1);
      while (n % p == 0) n /= p;
    }
  if (n > 1) ret = ret / n * (n - 1);
  return ret;
}
int tpow(int a, int t, int p) {
  int r = 1;
  bool f = false, o = false;
  for (; t; t >>= 1, o |= (long long)a * a >= p, a = (long long)a * a % p)
    if (t & 1) {
      f |= o;
      if ((long long)r * a >= p) f = true;
      r = (long long)r * a % p;
    }
  return r + (f ? p : 0);
}
int main() {
  gi(n), gi(p);
  for (int i = 1; i <= n; i++) gi(num[i]);
  while (p > 1) mod[m++] = p, p = phi(p);
  mod[m] = 1;
  gi(q);
  for (int i = 1, l, r; i <= q; i++) {
    gi(l);
    gi(r);
    if (r > l + m) r = l + m;
    ans = 1;
    for (int p = r; p >= l; p--) ans = tpow(num[p], ans, mod[p - l]);
    printf("%d\n", ans % *mod);
  }
  return 0;
}