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 Main {

	public static void main(String[] args) {
		// TODO Auto-generated method stub

		
		int members,binary_length,differ;
		Scanner sc = new Scanner(System.in);
		String str;
		String spstr[];
		int friend=0;
		String standard; //saving Ferdor's soldier type
		String b_type[]; // saving binary codes
		int raw_type[]; // saving number of binary codes
		
		binary_length = sc.nextInt();
		
		members = sc.nextInt();
		members++;
		
		differ = sc.nextInt();
		
		b_type = new String[members];
		raw_type = new int[members];
		
		for(int i=0;i<members;i++) {
			
			raw_type[i] = sc.nextInt();
			
		}
		
		//입력 완료
		
		
		//System.out.println("gd");
		
		for(int i=0;i<members;i++) {
			
			
			b_type[i] = Integer.toBinaryString(raw_type[i]);
		//	System.out.println(b_type[i].length());
			
		}
		
		
		//바이너리 변환 완료
		
		
		
		for(int i=0;i<members;i++) {
			
			if(b_type[i].length() != binary_length) {
				
				int size = binary_length - b_type[i].length();
				String zero_str="";
				for(int j=0;j<size;j++) {
					
					zero_str += "0";
					
				}
				
				b_type[i] = zero_str + b_type[i];
				
			}
			//System.out.println(b_type[i]);
		}
		
		//바이너리에 0 보충 완료
		
		standard = b_type[members-1];
		

		for(int i=0;i<members-1;i++) {
			
			int different=0;
			
			for(int j=0;j<binary_length;j++) {
				
				if(standard.charAt(j) != b_type[i].charAt(j))
					different++;
			
				}
			
			if(different <= differ)
				friend++;
			
		}
		
		
		System.out.println(friend);
		
		
	}

}