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 {
	static BufferedReader br;
	static PrintWriter pw;
	static StringTokenizer st;

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

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

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

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

	public static void main(String[] args) throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
				System.out)));
		// for (int i =1; i <= 111; i++) {
		// System.out.println(i+" "+Integer.toBinaryString(i));
		// }
		long n = nextLong();
		long m = nextLong();
		long k = nextLong();
		long x[] = new long[(int) m + 1];
		for (int i = 0; i <= m; i++) {
			x[i] = nextLong();
		}
		int ans = 0;
		for (int i = 0; i < m; i++) {
			if (Long.bitCount(Math.abs(x[i] ^ x[(int) m])) <= k)
				ans++;
		}
		pw.print(ans);
		pw.close();
	}

	private static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}

	static class Sort implements Comparable<Sort> {
		int y, z;

		public int compareTo(Sort arg0) {
			if (this.y != arg0.y)
				return -this.y + arg0.y;
			else
				return this.z - arg0.z;
		}
	}
}