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 Solution {
    public static void main(String[] args) {
	Scanner sc = new Scanner(System.in);
	int n = sc.nextInt();
	int m = sc.nextInt();
	int k = sc.nextInt();
	int[] x = new int[m + 1];
	for (int i = 0; i < m + 1; i++) {
	    x[i] = sc.nextInt();
	}
	int u = 0;
	for (int i = 0; i < m; i++) {
	    int f = x[i] ^ x[m];
	    int s = 0;
	    for (char c : Integer.toBinaryString(f).toCharArray()) {
		if (c == '1') {
		    s++;
		    if (s > k) {
			break;
		    }
		}
	    }
	    if (s <= k)
		u++;
	}
	System.out.println(u);
	sc.close();
    }
}