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.*;
import java.lang.*;
// import java.math.BigInteger;

public class praccf
{
    // public static int n;
    // public static int AP;
    // public static long DP[][];
    // public static ArrayList<ArrayList<Integer>> revmap;
    // public static int M = 1000000007;
    public static void main(String[] args) throws IOException{
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));  
        String[] l = in.readLine().split(" ");
        int n = Integer.parseInt(l[0]);
        int m = Integer.parseInt(l[1]);
        int k = Integer.parseInt(l[2]);
        int[] mat = new int[m + 1];
        for(int i=0;i<=m;i++){
            mat[i] = Integer.parseInt(in.readLine().trim());
        }
        int count = 0 , fredor = mat[m];
        for(int i=0;i<m;i++){
            if(Integer.bitCount(fredor^mat[i]) <= k){
                count++;
            }
        }
        System.out.println(count);
    }
    
}