Problem: After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game «Call of Soldiers 3».

The game has (m + 1) players and n types of soldiers in total. Players «Call of Soldiers 3» are numbered form 1 to (m + 1). Types of soldiers are numbered from 0 to n - 1. Each player has an army. Army of the i-th player can be described by non-negative integer xi. Consider binary representation of xi: if the j-th bit of number xi equal to one, then the army of the i-th player has soldiers of the j-th type. 

Fedor is the (m + 1)-th player of the game. He assume that two players can become friends if their armies differ in at most k types of soldiers (in other words, binary representations of the corresponding numbers differ in at most k bits). Help Fedor and count how many players can become his friends.

Input

The first line contains three integers n, m, k (1 ≤ k ≤ n ≤ 20; 1 ≤ m ≤ 1000).

The i-th of the next (m + 1) lines contains a single integer xi (1 ≤ xi ≤ 2n - 1), that describes the i-th player's army. We remind you that Fedor is the (m + 1)-th player.

Output

Print a single integer — the number of Fedor's potential friends.

Examples

Input

7 3 1
8
5
111
17


Output

0


Input

3 3 3
1
2
3
4


Output

3

Solution (in JAVA):

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

public class B {

	public static void main(String args[]) {
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		int m = in.nextInt();
		
		int k = in.nextInt();
		
		int[] list = new int[m+1];
		
		for(int i =0; i < m+1; i++ ) {
			list[i] = in.nextInt();
		}
			
		int me = list[m];
		
		int ans = 0;
		for( int i = 0; i < m; i++ ) {
			int you = list[i];
			
			int diff = me ^ you;
			
			int count = 0;
			
			while(diff > 0) {
				if(diff%2 == 1) {
					count++;
				}
				
				diff = diff>>1;
			}
			
			if( count <= k ) {
				ans ++;
			}
		}
		
		System.out.println(ans);
		
	}
	
}