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) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();
		char[][] binary = new char[m+1][n];
		for(int i=0;i<m+1;i++) {
			int temp = sc.nextInt();
			int j=n-1;
			boolean flag = false;
			while(temp!=1) {
				binary[i][j]=(char) ((temp%2)+'0');
				temp/=2;
				j--;//이진수로 바꾼 값 넣기
	
			}
			if(temp==1) {
				binary[i][j]='1';
				flag=true;
				j--;
				//끝나는 부분에 1 넣고
			}
			while(flag==true&&j>=0) {
					binary[i][j]='0';
					j--;
				} //나머지 앞부분에 0으로 채우기
			
			
		}

		int total=0;
		for(int i=0;i<m;i++) {
			int Bit=0;
			for(int j=0;j<n;j++) {
				if(binary[m][j]!=binary[i][j]) Bit++;
				//숫자 다를 때마다 추가
				
			}
			if(Bit<=k) total++;
			
		}
		System.out.println(total);

	}

}