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 MAIN {

	public static void main(String[] args) {

		Scanner scan = new Scanner(System.in);
		String line1 = scan.nextLine();
		String[] line11 = line1.split("\\s+");
		int n = Integer.parseInt(line11[0]);
		int m = Integer.parseInt(line11[1]);
		int k = Integer.parseInt(line11[2]);

		Integer[] lines = new Integer[m + 1];

		for (int i = 0; i < m + 1; i++) {

			lines[i] = scan.nextInt();

		}
		scan.close();
		String[][] lines1 = new String[m + 1][n];
		lines1[m] = intToBooleanArray(lines[m], n);
		Integer[] count = new Integer[m + 1];

		for (int i = 0; i < m + 1; i++) {
			count[i] = 0;
		}

		int d = 0;
		for (int i = 0; i < m; i++) {
			lines1[i] = intToBooleanArray(lines[i], n);
			d = lines1[m].length - lines1[i].length;
			if (d >= 0) {
				for (int j = 0; j < d; j++) {
					// System.out.println(count[i]);
					if (lines1[m][j].equals("1"))
						count[i]++;
					// System.out.println(count[i]);
				}
				for (int j = 0; j < lines1[i].length; j++) {
					// if(lines1[i][j]==null) lines1[i][j]="0";
					if (!(lines1[i][j].equals(lines1[m][j + d]))) {

						// System.out.println(lines1[i][j]+" "+lines1[m][j+d]);

						count[i]++;
					}
				}
			} else {
				for (int j = 0; j < -d; j++) {
					if (lines1[i][j].equals("1"))
						count[i]++;
				}
				for (int j = 0; j < lines1[m].length; j++) {
					// if(lines1[i][j]==null) lines1[i][j]="0";
					if (!(lines1[i][j - d].equals(lines1[m][j]))) {
						// System.out.println(lines1[i][j-d]+" "+lines1[m][j]);
						count[i]++;
					}
				}
			}
			// System.out.println(count[i].intValue());
		}
		int out = 0;
		for (int i = 0; i < m; i++) {
			if (count[i] <= k)
				out++;
		}

		System.out.print(out);

	}

	public static String[] intToBooleanArray(int num, int n) {

		String s = Integer.toBinaryString(num);
		// System.out.println(s);
		String[] s1 = new String[n];
		s1 = s.split("(?!^)");

		return s1;
	}
}