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.io.*;
import java.util.*;



public class A395 {

	

	public static void main(String[] args) throws IOException {
		solve();
	}
	
	
	static void solve() throws IOException {
		BufferedReader in;
		PrintWriter out;
		try {
			in = new BufferedReader(new FileReader("are1231a.in"));
			out = new PrintWriter(new File("are2131a.out"));
		} catch (Exception e) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(new OutputStreamWriter(System.out));
		}

		StringTokenizer tok = new StringTokenizer(in.readLine());
		int n = Integer.valueOf(tok.nextToken());
		int m = Integer.valueOf(tok.nextToken());
		int k = Integer.valueOf(tok.nextToken());
		int dig[][] = new int[m+1][2];
		int res = 0;
		int a = 0;
		for (int i = 0; i <= m; i++) {
			tok = new StringTokenizer(in.readLine());
			a = Integer.valueOf(tok.nextToken());
			dig[i][0] = a;
		}
		int f = dig[m][0];
		int f1 = 0;
		int raz = 0;
		for (int i = 0; i < m; i++) {
			f1 = dig[i][0];
			if (f1 > f) {
				int tmp = f1;
				f1 = f;
				f = tmp;
			}
			//System.out.println(f+" "+f1);
			while (f > 0) {
				if (f%2 != f1%2) raz++;
				f >>= 1;
				f1 >>= 1;
				
			}
			dig[i][1] = raz;
			raz = 0;
			f = dig[m][0];
		}
		//int res = 0;
		for (int i = 0; i < m; i++) {
			//System.out.println(dig[i][1]);
			if(dig[i][1] <= k) res++; 
		}
		System.out.println(res);
	}

}