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;
const int MAXN = 2e5 + 51;
struct Item {
  int x, flg;
};
struct BIT {
  int x[MAXN];
  inline void add(int pos, int val);
  inline int query(int pos);
};
BIT bit;
unordered_map<int, int> mp;
int n, qcnt, MOD, x, l, r;
inline int read() {
  register int num = 0, neg = 1;
  register char ch = getchar();
  while (!isdigit(ch) && ch != '-') {
    ch = getchar();
  }
  if (ch == '-') {
    neg = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    num = (num << 3) + (num << 1) + (ch - '0');
    ch = getchar();
  }
  return num * neg;
}
inline Item qpow(int base, int exponent, int MOD) {
  int res = 1, flg = 0;
  while (exponent) {
    if (exponent & 1) {
      flg |= ((long long int)res * base >= MOD),
          res = (long long int)res * base % MOD;
    }
    flg |= ((long long int)base * base >= MOD),
        base = (long long int)base * base % MOD, exponent >>= 1;
  }
  return (Item){res, flg};
}
inline void BIT::add(int pos, int val) {
  for (; pos <= n; pos += pos & -pos) {
    x[pos] += val;
  }
}
inline int BIT::query(int pos) {
  int res = 0;
  for (; pos; pos -= pos & -pos) {
    res += x[pos];
  }
  return res;
}
inline int phi(int x) {
  int res = x;
  for (register int i = 2; i <= sqrt(x); i++) {
    x % i == 0 ? res = res / i * (i - 1) : 1;
    while (x % i == 0) {
      x /= i;
    }
  }
  return x != 1 ? res / x * (x - 1) : res;
}
inline Item query(int l, int r, int p) {
  Item it;
  int x;
  if (p == 1 || l == r) {
    return p == 1 ? (Item){0, 1} : (x = bit.query(l), (Item){x % p, x >= p});
  }
  it = query(l + 1, r, mp[p]), x = it.x + it.flg * mp[p];
  return qpow(bit.query(l), x, p);
}
int main() {
  n = read(), x = MOD = read();
  while (x != 1) {
    x = (mp[x] = phi(x));
  }
  for (register int i = 1; i <= n; i++) {
    x = read(), bit.add(i, x), bit.add(i + 1, -x);
  }
  qcnt = read();
  for (register int i = 1; i <= qcnt; i++) {
    l = read(), r = read(), printf("%d\n", query(l, r, MOD).x);
  }
}