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.*;
import java.io.*;

public class Main {

private static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException e) {
                  e.printStackTrace();
              }
          }
          return st.nextToken();
      }

      int[] getIntArray(int k) {
        int[] a = new int[k];
        for (int j = 0; j < k; j++) a[j] = nextInt();
        return a;
      }

      long[] getLongArray(int k) {
        long[] a = new long[k];
        for (int j = 0; j < k; j++) a[j] = nextLong();
        return a;
      }
 
      int nextInt() {
          return Integer.parseInt(next());
      }
 
      long nextLong() {
          return Long.parseLong(next());
      }
 
      double nextDouble() {
          return Double.parseDouble(next());
      }
 
      String nextLine(){
          String str = "";
	  try {
	     str = br.readLine();
	  } catch (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }

}
  public static void main(String[] args) {
    MyScanner s = new MyScanner();
    int n = s.nextInt();
    int m = s.nextInt();
    int k = s.nextInt();
    int[] p = s.getIntArray(m+1);
    int[] nb = new int[p.length];
    for (int j = 0; j < m + 1; j++) {
      int c = 0; int d = p[j];
      while (d > 0) { if ((d & 1) == 1) c++; d = d/2; }
      nb[j] = c;
    }
    int f = 0;
    for (int j = 0; j < m; j++) {
      int d = p[j] & p[m];
      int c = 0;
      while (d > 0) {
        if ((d & 1) == 1) c++;
        d = d/2;
      }
      c = nb[j] + nb[m] - 2*c;
      if (c <= k) f++;
    }
    System.out.println(f);
  }
}