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:
/**
 * Created by ckboss on 14-9-19.
 */
import java.util.*;

public class FedorandNewGame {
    static int n,m,k,F;
    static int[] am = new int[1050];
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        n=in.nextInt(); m=in.nextInt(); k=in.nextInt();
        for(int i=1;i<=m;i++)
            am[i]=in.nextInt();
        F=in.nextInt();
        int ans=0;
        for(int i=1;i<=m;i++){
            int D=am[i]^F;
            int tp=0;
            while(D>0){
                if(D%2==1){
                    tp++;
                }
                D/=2;
            }
            if(tp<=k)
                ans++;
        }
        System.out.println(ans);
    }
}