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;
import java.io.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Scanner in = new Scanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {

	int NumberOfSetBits(int i)
	{
		i = i - ((i >>> 1) & 0x55555555);
		i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
		return (((i + (i >>> 4)) & 0x0F0F0F0F) * 0x01010101) >>> 24;
	}


    public void solve(int testNumber, Scanner in, PrintWriter out) {
		int n = in.nextInt();
		int m = in.nextInt();
		int k = in.nextInt();
		int[] mem = new int[m + 1];
		for (int i = 0; i < m + 1; i++) {
			mem[i] = in.nextInt();
		}
		int fedor = mem[m];
		int c = 0;
		for (int i = 0; i < m; i++) {
			int temp = fedor ^ mem[i];
			int count = NumberOfSetBits(temp);
			if (count <= k){
				c++;
			}
		}
		out.println(c);
	}
}