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.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.*;
import java.io.*;
public class Main {
    public static void main(String args[])throws Exception{
        Input sc=new Input();
        StringBuilder sb=new StringBuilder();
        //int t=sc.readInt();
        for(int f=0;f<1;f++){
            int d[]=sc.readArray();
            int n=d[0];
            int m=d[1];
            int k=d[2];
            int arr[]=new int[m+1];
            for(int i=0;i<=m;i++){
                arr[i]=sc.readInt();
            }
            int count=0;
            for(int i=0;i<m;i++){
                int temp=arr[m]^arr[i];
                int c=0,l=1,g=1;
                while(temp>0){
                    if((temp&l)!=0){
                        c+=1;
                    }
                    //l=l<<1;
                    //System.out.println(l);
                    g++;
                    temp/=2;
                }
                if(c<=k)
                    count++;
               // System.out.println("----------");
            }
            sb.append(count+"\n");
        }
        System.out.print(sb);
    }
}
class Input{
    BufferedReader br;
    StringTokenizer st;
    Input(){
        br=new BufferedReader(new InputStreamReader(System.in));
        st=new StringTokenizer("");
    }
    public int[] readArray() throws Exception{
        st=new StringTokenizer(br.readLine());
        int a[]=new int[st.countTokens()];
        for(int i=0;i<a.length;i++){
            a[i]=Integer.parseInt(st.nextToken());
        }
        return a;
    }
    public long[] readArrayLong() throws Exception{
        st=new StringTokenizer(br.readLine());
        long a[]=new long[st.countTokens()];
        for(int i=0;i<st.countTokens();i++){
            a[i]=Long.parseLong(st.nextToken());
        }
        return a;
    }
    public int readInt() throws Exception{
        st=new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }
    public long readLong() throws Exception{
        st=new StringTokenizer(br.readLine());
        return Long.parseLong(st.nextToken());
    }
    public String readString() throws Exception{
        return br.readLine();
    }
    public int[][] read2dArray(int n,int m)throws Exception{
        int a[][]=new int[n][m];
        for(int i=0;i<n;i++){
            st=new StringTokenizer(br.readLine());
            for(int j=0;j<m;j++){
                a[i][j]=Integer.parseInt(st.nextToken());
            }
        }
        return a;
    }
}