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.*;
public class FedorandNewGame {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc= new Scanner(System.in);
		int n=sc.nextInt(),m=sc.nextInt(),k=sc.nextInt();
		int a[]=new int[m+1];
		for(int i=0;i<=m;i++)
			a[i]=sc.nextInt();
		int h=0; String t=(Integer.toBinaryString(a[m])); 
		//System.out.println(t);
		for(int i=0;i<m;i++)
		{
			String s=Integer.toBinaryString(a[i]); //System.out.println(s);
			int x=s.length()-1,c=0, y=t.length()-1; //System.out.println("x= "+x+" y= "+y+" c= "+c);
			while(y>=0&&x>=0)
			{
				if(s.charAt(x)!=t.charAt(y))
					c++;
				y--; x--;
			} //System.out.println("x= "+x+" y= "+y+" c= "+c);
			while(y>=0) 
			{
				if(t.charAt(y)=='1')
					c++;
				y--;
			}   //System.out.println("x= "+x+" y= "+y+" c= "+c);
			while(x>=0)
			{
				if(s.charAt(x)=='1') c++;
				x--;
			} //System.out.println("x= "+x+" y= "+y+" c= "+c);
			if(c<=k) h++;
		}
		System.out.println(h);
	}

}