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.BufferedInputStream;
import java.util.Scanner;

/**
 * Created by jizhe on 2015/12/22.
 */
public class FedorAndNewGame {
    public static void main(String[] args) {
        Scanner in = new Scanner(new BufferedInputStream(System.in));

        int N = in.nextInt();
        int M = in.nextInt();
        int K = in.nextInt();
        int[] armies = new int[M+1];
        for( int i = 0; i < M+1; i++ )
        {
            armies[i] = in.nextInt();
        }
        int f = armies[M];

        int count = 0;
        for( int i = 0; i < M; i++ )
        {
            int result = f ^ armies[i];
            int k = 0;
            if( (result & 0x01) == 1 )
            {
                k++;
            }
            for( int j = 1; j < N; j++ )
            {
                result = result >> 1;
                if( (result & 0x01) == 1 )
                {
                    k++;
                }
            }
            if( k <= K )
            {
                count++;
            }
        }

        System.out.printf("%d\n", count);
    }

}