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 apples{
	public static void main(String[]args) {
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int m=sc.nextInt();
		int k=sc.nextInt();
		String x[]=new String[m+1];
		for (int i=0;i<m;i++) {
			x[i]=Integer.toBinaryString(sc.nextInt());
			if (x[i].length()<n) {
				while(x[i].length()!=n)
					x[i]="0"+x[i];
			}
		}
		int sama7=0;
		int friend=0;
		x[m]=Integer.toBinaryString(sc.nextInt());
		while(x[m].length()!=n)
			x[m]="0"+x[m];
		for (int i=0;i<m;i++) {
			for (int j=0;j<x[i].length();j++) {
				if (x[m].charAt(j)!=x[i].charAt(j)) {
					sama7++;
					if (sama7>k) {
						break;
					}
				}
			}
			if (sama7<=k)
				friend++;
			sama7=0;
		}
		System.out.println(friend);
	}
}