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 JAVA):

Solution:
import java.util.*;
import java.io.IOException;

public class Test {
    int readInt() {
        int ans = 0;
        boolean neg = false;
        try {
            boolean start = false;
            for (int c = 0; (c = System.in.read()) != -1; ) {
                if (c == '-') {
                    start = true;
                    neg = true;
                    continue;
                } else if (c >= '0' && c <= '9') {
                    start = true;
                    ans = ans * 10 + c - '0';
                } else if (start) break;
            }
        } catch (IOException e) {
        }
        return neg ? -ans : ans;
    }

    long m;
    final int N = 100_010;
    int[] power = new int[N];
    long[] phi = new long[64];

    long getPhi(long v) {
        long ans = v;
        for (int i = 2; i*i <= v; i++) {
            if (v % i == 0) {
                ans *= (i-1);
                ans /= i;
                while (v % i == 0) v /= i;
            }
        }
        if (v != 1) ans = ans*(v-1)/v;
        return ans;
    }

    long mod(long v, long m) {
        if (v < m) return v;
        return (v % m) + m;
    }

    long solve(int l, int r, int d) {
        if (l > r || phi[d] == 0) return 1;
        long e = solve(l + 1, r, d + 1);
        long ans = 1, v = power[l];
        while (e != 0) {
            if ((e & 1) != 0) ans = mod(ans * v,  phi[d]);
            v = mod(v*v, phi[d]);
            e >>>= 1;
        }
        return ans;
    }

    void start() {
        int n = readInt(), m = readInt();
        for (int i = 1; i <= n; i++) power[i] = readInt();
        phi[0] = m;
        for (int i = 0; phi[i] != 1; i++) phi[i+1] = getPhi(phi[i]);
        int q = readInt();
        while (q-- > 0) {
            int l = readInt(), r = readInt();
            System.out.println((l == r ? power[l] : solve(l, r, 0)) % m);
        }
    }

    public static void main(String[] args) {
        new Test().start();
    }
}