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.*;
import java.lang.*;

public class Rextester{
    public static boolean valid(int a,int b,int k){
        int army1 = Integer.bitCount(a);
        int army2 = Integer.bitCount(b);
        int armyCommon = Integer.bitCount(a&b);
        if((army1+army2-2*armyCommon)>k){
            return false;
        }
        return true;
    }
        
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int n = new Integer(st.nextToken());
        int m= new Integer(st.nextToken());
        int k = new Integer(st.nextToken());
        int[] players = new int[m+1];
        for(int i=0;i<m+1;i++){
            players[i]=new Integer(br.readLine());
        }
        br.close();
        int friend = 0;
        for(int i=0;i<m;i++){
            if(valid(players[i],players[m],k)){
                friend++;
            }
        }
        System.out.println(friend);
    }
}