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 FedorAndNewGame {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(), m = sc.nextInt(), k = sc.nextInt();
        int[] arr = new int[m];
        for(int i = 0; i<m; i++)arr[i]= sc.nextInt();
        int mask = sc.nextInt();
        int ans = 0;
        for(int x: arr){
            int temp = x ^ mask;
            int cnt = 0;
            for(int i = 0; i<21;i++){
                cnt += 1 & temp;
                temp = temp>>1;
            }
            if(cnt <= k)ans++;
        }
        System.out.println(ans);
    }

}