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.Scanner;
public class Fedor
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int m=sc.nextInt();
        int k=sc.nextInt();
        int arr[][]=new int[m+1][n];
        int count=0;
        for (int i=0;i<m+1;i++)
        {
            arr[i]=d_to_b(sc.nextInt(),n);
        }
        for (int i=0;i<m;i++)
        {
            int points=0;
            for (int j=0;j<n;j++)
            {
                if (arr[i][j]!=arr[m][j])
                {
                    points++;
                }
            }
            if (points<=k)
            {
                count++;
            }
        }
        System.out.println(count);
    }
    public static int[] d_to_b(int x,int n)
    {
        int b[]=new int[n];
        for (int i=0;i<n;i++)
        {
            b[i]=x%2;
            x=x/2;
        }
        return b;
    }
}