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 static java.lang.System.in;

import java.io.IOException;


public class B267 {
    
    static byte[] buffer = new byte[8192];
    static int offset = 0;
    static int bufferSize = 0;
    public static void main(String args[])throws IOException
    {
        int n =readInt();
        int m =readInt();
        int k =readInt();
        int arr[]= new int[m+1];
        for (int i=0;i<=m;i++)
            arr[i]= readInt();
        int ans=0;
        for (int i=0;i<m;i++)
        {
            int num = arr[m]^arr[i];
            int c=0;
            int arr1[] =new int[20];
            int arr2[]= new int[20];
            //System.out.println(arr[m-1]+" "+num);
            while(num!=0)
            {
                if ((num & 1)==1)
                    c++;
                num =num>>1;
            }
            if (c<=k)
                {
                //System.out.println( num +" "+i);
                ans++;
                }
        }
        System.out.println(ans);
        
    }
    
    
    static int readInt() throws IOException{
        int number = 0;
        int s =1;
        if(offset==bufferSize){
            offset = 0;
            bufferSize = in.read(buffer);
        }
        for(;buffer[offset]<0x30 || buffer[offset]=='-'; ++offset)
        {
            if (buffer[offset]=='-')
                s=-1;
            if(offset==bufferSize-1 ){
                offset=-1;
                bufferSize = in.read(buffer);
            }
        }
        for(;offset<bufferSize && buffer[offset]>0x2f;++offset){
            number = number*0x0a+buffer[offset]-0x30;
            if(offset==bufferSize-1){
                offset = -1;
                bufferSize = in.read(buffer);
            }
        }
        ++offset;
        return number*s;
    }

}