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 fedorandnewgame {
	static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

	public static void main(String[] args) throws IOException {
		String[] line = br.readLine().split(" ");
		int n = Integer.parseInt(line[0]);
		int m = Integer.parseInt(line[1]);
		int k = Integer.parseInt(line[2]);
		int[] arr = new int[m+1];

		for(int i = 0; i <= m; i++) {
			arr[i] = Integer.parseInt(br.readLine());
		}

		int fedor = arr[m];
		int count = 0;

		for(int i = 0; i < m; i++) {
			int diff = (fedor ^ arr[i]);
			// System.out.println(Integer.toBinaryString(fedor));
			// System.out.println(Integer.toBinaryString(arr[i]));
			// System.out.println(Integer.toBinaryString(diff));
			// System.out.println("=====================");
			int numOnes = Integer.bitCount(diff);
			// if(Integer.toBinaryString(Math.max(fedor,arr[i])).length()-numOnes <= k) {
			if(numOnes <= k) {
				count++;
			}
		}

		bw.write(count+ "\n");
		bw.close();
	}

}