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.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class B {
	private static BufferedReader in;
	private static StringTokenizer st;
	private static PrintWriter out;

	public static void main(String[] args) throws NumberFormatException, IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		st= new StringTokenizer("");
		out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = nextInt();
		int m = nextInt();
		int k = nextInt();
		int ans = 0;
		int a[] = new int [m+2];
		for (int i = 1; i <=m+1; i++) {
			a[i] = nextInt();
		}
		for (int i = 1; i <=m; i++) {
			int or = a[m+1] | a[i], and = a[m+1] & a[i];
			int t = 0;
			for (int j = 0; j < n; j++) {
				if((or & (1<<j)) > 0){
					t++;
				}
				if((and & (1<<j)) > 0){
					t--;
				}
			}
			if(t >=0 && t<=k){
				ans++;
			}
		}
		System.out.println(ans);
		out.close();
	}

	private static double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(next());
	}

	private static long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(next());
	}

	private static int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(next());
	}

	private static String next() throws IOException {
		while(!st.hasMoreTokens())
			st = new StringTokenizer(in.readLine());
		return st.nextToken();
	}
}