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.util.*;
import java.io.*;
public class Prac {
	
	static int count=0;
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		PrintStream ps=System.out;

		int n=sc.nextInt(), m=sc.nextInt(), k=sc.nextInt();
		int[] nums=new int[m+1];

		for(int i=0; i<m+1; i++)
			nums[i]=sc.nextInt();

		int ans=0;
		for(int i=0; i<m; i++){
			int num=nums[i]^nums[m];
			int c=0;
			for(int j=0; j<n; j++){
				if(num%2==1) c++;
				num=num>>1;
			}
			if(c<=k) ans++;
		}

		ps.println(ans);

	}

	/*public static int reverse(int num, int n){
		int ans=0;
		for(int i=0; i<n; i++){
			ans=ans*2+num/2;
			num=num>>1;
		}
		return ans;
	}*/

	}