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:
//package Atcoder;
import java.io.*;
import java.util.*;
 
 
public class wtf {
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		String inp[]=br.readLine().split(" ");
		int n=Integer.parseInt(inp[0]);
		int m=Integer.parseInt(inp[1]);
		int k=Integer.parseInt(inp[2]);
		String[] binary=new String[m+1];
		for(int i=0;i<m+1;i++) {
			binary[i]=Integer.toBinaryString(Integer.parseInt(br.readLine()));
		}
		int answer=0;
		for(int i=0;i<m;i++) {
			if(diff(binary[i],binary[m])<=k) {
				answer++;
//				System.out.println("friends with:"+binary[i]+" and,:"+binary[m]);
			}
		}
		System.out.println(answer);
	}
	public static int diff(String a,String b) {
		int ans=0;
		int la=a.length();
		int lb=b.length();
		int limit=Math.min(la,lb);
		int i;
		for(i=0;i<limit;i++) {
			if(a.charAt(la-1-i)!=b.charAt(lb-i-1)) {
//				System.out.println("diff found");
				ans++;
			}
		}
//		i--;
		String tocheck;
		if(la<lb) {
			limit=lb;
			tocheck=b;
		}
		else if(lb<la) {
			limit=la;
			tocheck=a;
		}
		else return ans;
		while(i<limit) {
			if(tocheck.charAt(limit-i-1)=='1') {
				ans++;
//				System.out.println("diff found here");
			}
			i++;
		}
//		System.out.println("returned");
		return ans;
	}
}