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 b267{
public static void main(String args[]){
Scanner in =new Scanner(System.in);
int n,m,k,fr=0;
n=in.nextInt();
m=in.nextInt();
k=in.nextInt();
int a[]=new int[m+1];
for(int i=0;i<m+1;i++){
a[i]=in.nextInt();
}
for(int i=0;i<m;i++){
fr=fr+frn(a[i],a[m],k,n);
}
System.out.print(fr);
}
public static int frn(int a,int b,int k,int n){

String c=""+Integer.toString(a,2);
while(c.length()<n)
c="0"+c;
String d=""+Integer.toString(b,2);
while(d.length()<n)
d="0"+d;
int cn=0;
for(int i=0;i<n;i++){
if(c.charAt(i)!=d.charAt(i))
   cn++;
 }
if(cn<=k)
 return 1;
else
return 0;
}}