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.Scanner;
import java.util.Arrays;
public class Cf5{
    public static void main(String args[]){
        Scanner s = new Scanner(System.in);
        int n,m,k,i,j,f=0;
         n = s.nextInt();
         m = s.nextInt();
         k = s.nextInt();
         int x[] = new int[m+1];
         for(i=0 ; i<=m ; i++){
             x[i] = s.nextInt();
         }
         int a[][] = new int[m+1][n];
         for(i=0 ; i<=m ; i++){
             j=0;
            while(x[i] >0){
                int d = x[i]%2;
                a[i][j] = d ;
                x[i] = x[i]/2;
                j++;
            }
        }
        for(i=0 ; i<m ; i++){
            int z=0;
            for(j=0 ; j<n ; j++){
                if (a[m][j] != a[i][j] ){
                     z++;
                }
            }
            if(z<=k){
                f++;
            }
        }
        System.out.println(f);
    }
}