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.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class B {

  static InputReader in;
  static PrintWriter out;

  static int n;

  static void solve() {
    n = in.ni();
    int m = in.ni();
    int k = in.ni();

    String[] x = new String[m + 1];

    for (int i = 0; i < m + 1; i++) {
      String s = Integer.toBinaryString(in.ni());
      while (s.length() != n) {
        s = '0' + s;
      }
      x[i] = s;
    }

    int count = 0;

    for (int i = 0; i < m; i++) {
      if (diff(x[i], x[m]) <= k) {
        count++;
      }
    }

    out.println(count);
  }

  static int diff(String player, String opponent) {
    int count = 0;

    for (int i = 0; i < n; i++) {
      if (player.charAt(i) != opponent.charAt(i)) {
        count++;
      }
    }

    return count;
  }

  public static void main(String[] args) throws IOException {
    InputStream is = System.in;
    PrintWriter out = new PrintWriter(System.out);

    run(is, out);

    is.close();
    out.close();
  }

  static void run(InputStream is, PrintWriter pw) {
    in = new InputReader(is);
    out = pw;
    solve();
  }

  static class InputReader {
    BufferedReader br;
    StringTokenizer st;

    InputReader(InputStream stream) {
      br = new BufferedReader(new InputStreamReader(stream));
    }

    String next() {
      while (st == null || !st.hasMoreElements()) {
        try {
          String line = br.readLine();
          if (line == null) {
            return null;
          }
          st = new StringTokenizer(line);
        } catch (IOException e) {
          e.printStackTrace();
        }
      }
      return st.nextToken();
    }

    int ni() {
      return Integer.parseInt(next());
    }

    long nl() {
      return Long.parseLong(next());
    }

    int[] na(int n) {
      int[] arr = new int[n];
      for (int i = 0; i < n; i++) {
        arr[i] = ni();
      }
      return arr;
    }
  }
}