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 codechef
{
    public static void main(String args[])
    {
       Scanner x = new Scanner(System.in);
       int n = x.nextInt();
       int m = x.nextInt();
       int k = x.nextInt();
       int i;
       int arr[] = new int[m+1];
       for(i =0;i<m+1;i++)
       {
       	arr[i]= x.nextInt();
       }
       int sum =0;
       int tn,tk;
       for(i=0;i<m;i++)
       {
       	tn =n;
       	tk = k;
       	int y = arr[m];
       	while(--tn>=0)
       	{
       		if(arr[i]%2!=y%2)
       		{
       			tk--;
       		}
       		arr[i]/=2;
       		y/=2;
       	}
       	if(tk>=0)
       	{
       		sum++;
       	}
       }
       System.out.println(sum);
    }
}