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;
import java.util.*;
import java.lang.*; 
import java.util.regex.Pattern;
import java.text.DecimalFormat;
import java.util.stream.IntStream;
public class Main{ 
static int isOn(int S, int j) { return S & (1 << j); }
static int a,b,c;
static int[] dp=new int[4010];
static final int INF=1000000;  
public static void main(String[] args)
{
Scanner scanner=new Scanner(System.in);
int n=scanner.nextInt();
int m=scanner.nextInt();
int k=scanner.nextInt();
int[] a=new int[m+1];
int count=0;
for(int i=0;i<m+1;i++)a[i]=scanner.nextInt();
for(int i=0;i<m;i++)
{	int sum=0;
    int x=a[i]^a[m];
    for(int j=0;j<n;j++)
    	if(isOn(x,j)>0)sum++;
    if(sum<=k)count++;
}
System.out.println(count);
}
}