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 B267 {

	public static void main(String[] args) {

		Scanner in = new Scanner(System.in);

		int n = in.nextInt();
		int m = in.nextInt();
		int k = in.nextInt();
		int ans = 0;
		int arr[] = new int[m];
		for (int i = 0; i < m; i++) {
			arr[i] = in.nextInt();
		}
		int fedorArmy = in.nextInt();
		String fedor = Integer.toBinaryString(fedorArmy);
		int len = fedor.length();
		String tmp="";
		for (int i = 0; i < n - len; i++) {
			tmp+="0";

		}
		fedor=tmp+fedor;
		for (int i = 0; i < m; i++) {
			int x = arr[i];
			String bin = Integer.toBinaryString(x);
			 len=bin.length();
			 tmp="";
			 for (int q = 0; q < n - len; q++) {
					tmp+="0";

				}	 
			 bin=tmp+bin;
			int diff=0;
			 for (int j = 0; j < n; j++) {
				if(fedor.charAt(j)!=bin.charAt(j))
					diff++;
			}
			 if(diff<=k)
				 ans++;
			 diff=0;
		}
		System.out.println(ans);
	}
}