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.*;
public class fedor
{
    static Scanner sc=new Scanner(System.in);
    public static void main(String args[])
    {
        long n=sc.nextInt();
        long m=sc.nextInt();
        long k=sc.nextInt();
        long a[]=new long[(int)m+1];
        long counter=0;
        for(long i=0;i<m+1;i++)
        {
            a[(int)i]=sc.nextInt();
        }
        for(long i=m-1;i>=0;i--)
        {
            long x=a[(int)m]^a[(int)i];
            long c=countSetBits(x);
            if(c<=k)
            {
                counter++;
            }
        }
        System.out.println(counter);
    }
    static long countSetBits(long n)
    {
        long count=0;
        while(n>0)
        {
            n=n&(n-1);
            count++;
        }
        return count;
    }
}