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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class f {
	

	public static void main(String args[]) throws IOException {
		FastScanner in = new FastScanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		//BEGIN HERE
		int n = in.nextInt();
		long mod = in.nextLong();
		phi[0] = mod;
		primes = new ArrayList<>();
		primes.add((long) 2);
		long p = 3;
		while(primes.get(primes.size() - 1) * primes.get(primes.size() - 1) <= mod) 
		{
			if(BigInteger.valueOf(p).isProbablePrime(100)) primes.add(p);
			p++;
		}
		for(int i = 1; i < 100; i++) {
			phi[i] = totient(phi[i-1]);
			if(phi[i] == 1) break;
		}
		numbers = new long[n];
		for(int i = 0; i < n; i++) numbers[i] = in.nextLong();
		int q = in.nextInt();
		for(int i = 0; i < q; i++) {
			int l = in.nextInt() - 1;
			int r = in.nextInt() - 1;
			System.out.println(solve(l, r, 0) % mod);
		}
		out.close();
	}
	static long phi[] = new long[100];
	static long numbers[];

	static long mod(long v, long m) {
		if (v < m)
			return v;
		return (v % m) + m;
	}
	static long solve(int l,int r,int p) {
		if(l > r || phi[p] == 0) return 1;
		long e = solve(l + 1 , r, p + 1);
		long v = numbers[l];
		long ans = 1;
		while(e != 0) {
			if((e & 1) != 0) ans = mod(ans * v, phi[p]);
			v = mod(v * v, phi[p]);
			e>>=1;
		}
		return ans;
	}
	
	static ArrayList<Long> primes;

	static long totient(long n){
		long phi = 1;
		for (long p : primes) {
			if(p*p > n) break;
			if (n % p != 0) continue;
			n /= p;
			phi *= p-1;
			while(n % p == 0) {
				phi *= p;
				n /= p;
			}
		}
		if(n != 1)
			phi *= n-1;
		return phi;
	}


	static class FastScanner {
		BufferedReader br;
		StringTokenizer st;

		public FastScanner(InputStream i) {
			br = new BufferedReader(new InputStreamReader(i));
			st = null;
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			if (st == null) {
				st = new StringTokenizer(br.readLine());
			}
			String line = st.nextToken("\n");
			st = null;
			return line;
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
	}

	public static class combinatorics {
		static long modInv(long a, long b) {
			return 1 < a ? b - modInv(b % a, a) * b / a : 1;
		}

		static long factorial[], mod;

		combinatorics(int n, long MOD) {
			mod = MOD;
			factorial = new long[n + 1];
			factorial[0] = 1;
			for (int i = 1; i <= n; i++) {
				factorial[i] = i * factorial[i - 1];
				factorial[i] %= mod;
			}
		}

		static long nCr(int n, int r) {
			if (r > n)
				return 0;
			return (factorial[n] * modInv((factorial[n - r] * factorial[r]) % mod, mod)) % mod;
		}
	}

	public static class DisjointSet {
		int p[], r[], s[];
		int numDisjoint;

		DisjointSet(int N) {
			numDisjoint = N;
			r = new int[N];
			s = new int[N];
			p = new int[N];
			for (int i = 0; i < N; i++)
				p[i] = i;
		}

		int findSet(int i) {
			return (p[i] == i) ? i : (p[i] = findSet(p[i]));
		}

		boolean isSameSet(int i, int j) {
			return findSet(i) == findSet(j);
		}

		void unionSet(int i, int j) {
			if (!isSameSet(i, j)) // if from different set
			{
				numDisjoint--;
				int x = findSet(i), y = findSet(j);
				if (r[x] > r[y]) {
					p[y] = x; // rank keeps the tree short
					s[x] += s[y];
				} else {
					p[x] = y;
					if (r[x] == r[y])
						r[y]++;
					s[y] += s[x];
				}
			}
		}

		int sizeOfSet(int i) {
			return s[findSet(i)];
		}
	};

}