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.*;

public class B1
{
    public static void main(String args[]) throws java.lang.Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));

        String S[]=br.readLine().split(" ");
        int n,m,k;
        n=Integer.parseInt(S[0]);
        m=Integer.parseInt(S[1]);
        k=Integer.parseInt(S[2]);

        int[] A1=new int[m+2];
        //String[] S1=new String[m+1];
        for(int i=1;i<=m+1;i++)
        {
            A1[i]=Integer.parseInt(br.readLine());
        }
        int K1,length,count=0,Total=0,length1,max,K2;
        for(int i=1;i<=m;i++)
        {
            count=0;
            K1=A1[i]^A1[m+1];
            String S1= Integer.toBinaryString(K1);
            length=S1.length();
            for(int j=0;j<length;j++)
            if(S1.charAt(j)=='1')
            count++;
            if(count<=k)
            Total++;
        }
        System.out.println(Total);
    }
}