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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;


import java.util.*;

public class A_GENERAL {

	public static void main(String[] args) {
		
		MyScanner sc = new MyScanner();
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();
		int[] a = new int[m];
		for(int i = 0; i < m; i++) {
			a[i] = sc.nextInt();
		}
		int fedor = sc.nextInt();
		int friends = 0;
		for(int i = 0; i < m; i++) {
			int x = fedor;
			int y = a[i];
			int diff = 0;
			while(x > 0 || y > 0) {
				if(x > 0 && y > 0) {
					if((x & 1) != (y & 1)) diff++;
					x >>= 1;
					y >>= 1;
				} else if(x > 0) {
					if((x & 1) == 1) diff++;
					x >>= 1;
				} else {
					if((y & 1) == 1) diff++;
					y >>= 1;
				}
			}
			if(diff <= k) friends++;
		}
		System.out.println(friends);
	}
	
	static class MyScanner {
		BufferedReader br;
		StringTokenizer st;
		public MyScanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		String next() {while (st == null || !st.hasMoreElements()) {
			try {st = new StringTokenizer(br.readLine());}
			catch (IOException e) {e.printStackTrace();}}
		return st.nextToken();}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() {return Double.parseDouble(next());}
		String nextLine(){String str = "";
		try {str = br.readLine();}
		catch (IOException e) {e.printStackTrace();}
		return str;}
	}
	
}
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