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.io.*;
import java.util.*;

public class P2 {
	public static void main (String[] args) {
		Scanner sc = new Scanner (System.in);
		PrintStream op = System.out;
		int n = sc.nextInt(), m = sc.nextInt(), k = sc.nextInt();
		int[] a = new int [m + 1];
		for (int i = 0; i < m + 1; i++)
			a[i] = sc.nextInt();
		int count = 0;
		for (int i = 0; i < m; i++) {
			int res = a[i] ^ a[m];
			int bC = 0;
			while (res > 0) {
				if ((res & 1) == 1)
					bC++;
				res = res >> 1;
			}
			if (bC <= k)
				count++;
		}
		op.println(count);
		
		sc.close();
	}
}