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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class TheodorGameProblem {

	public static void main(String[] args) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		StringTokenizer tokenizer = new StringTokenizer(in.readLine());

		Integer.parseInt(tokenizer.nextToken());
		int m = Integer.parseInt(tokenizer.nextToken());
		int k = Integer.parseInt(tokenizer.nextToken());
		int[] armies = new int[m + 1];

		for (int i = 0; i <= m; ++i) {
			tokenizer = new StringTokenizer(in.readLine());
			armies[i] = Integer.parseInt(tokenizer.nextToken());
		}

		int result = 0;
		int theodorsArmy = armies[m];
		for (int i = 0; i < m; ++i) {
			int xor = armies[i] ^ theodorsArmy;
			int diffCnt;
			for (diffCnt = 0; xor != 0; ++diffCnt) {
				xor &= xor - 1;
			}
			if (diffCnt <= k)
				++result;
		}
		out.print(result);
		out.flush();
	}

}