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 Prob467B {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int n = sc.nextInt(); // types of soldiers
		int m = sc.nextInt(); // players
		int k = sc.nextInt(); // differ types
		int friends = 0;
		
		int[] arr = new int[m+1];
		for(int i=0;i<arr.length;i++) {
			arr[i] = sc.nextInt();
		}
		
		int fedor = arr[m];
		
		for(int i=0;i<m;i++) {
			int res = arr[i] ^ fedor;
			int count = 0;
			char[] charArr = Integer.toBinaryString(res).toCharArray();
			for(int j=0;j<charArr.length;j++) {
				if(charArr[j] == '1') count++;
			}
			if(count<=k) {
				friends++;
			}
		}
		
		
		System.out.println(friends);
		
		
	}
}