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:
//package algoEx;

import java.util.Scanner;

public class FedorAndNewGame {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		int bit=0,player=0,num=0;
		Scanner scan = new Scanner(System.in);
		bit=scan.nextInt();
		player=scan.nextInt();
		num=scan.nextInt();
		
		int[] pData=new int[player+1];
		
		for(int i=0;i<player+1;i++){
			pData[i]=scan.nextInt();
		}
		
		int[][] bit2 = new int[player+1][bit];
		//2����
		for(int i=0;i<player+1 ;i++){
			int  j=0;
			while(true){
				if(pData[i]==1){
					bit2[i][j]=1;
					break;
				}
				bit2[i][j]=pData[i]%2;
				pData[i] = pData[i]/2;
				j++;
				if(pData[i]==1){
					bit2[i][j]=1;
					break;
				}
				
			}
		}
		//���
		/*for(int i=0; i<player+1 ; i++){
			for(int j=0; j<bit;j++){
				System.out.print(bit2[i][j]);
			}
			System.out.println();
		}*/
		
		int result=0;
		for(int i=0; i<player ; i++){
			int cnt=0;
			for(int j=0;j<bit ; j++){
				if(bit2[player][j]!=bit2[i][j]){
					cnt++;
				}
			}
			if(cnt <= num){
				result++;
			}
			
		}
		System.out.println(result);
	}

}