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 Sample {

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt(),m = sc.nextInt(),k = sc.nextInt();
        long a[] = new long[m+1];
        for(int i=0;i<=m;i++)
            a[i] = sc.nextLong();
        long x = a[m],count=0;
        for(int i=0;i<m;i++){
            int check =0 ;
             x = a[m];
            while(a[i]!=0||x!=0){
                int r1=0,r2=0;
                if(a[i]>0)
                 r1 = (int)a[i]%2;
                if(a[m]>0)
                 r2 = (int)x%2;
                if(r1!=r2)
                    check++;
                if(check>k)
                    break;
                a[i]/=2;
                x/=2;
            }
             if(check<=k)
             {
                // System.out.println(i);
                 count++;
             }
        }
        System.out.println(count);
    }
}