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.*;

public class MyClass {
    public static void main(String args[]) {
      Scanner s = new Scanner(System.in);
      int n = s.nextInt();
      int m = s.nextInt();
      int k = s.nextInt();
      ArrayList<Integer> arr = new ArrayList<Integer>();
      while(m-->0){
          int p =s.nextInt();
          arr.add(p);
      }
      //System.out.println()
      int u = s.nextInt();
      int ans = 0;
      for(int i=0 ;i<arr.size();i++){
          int q = arr.get(i)^u;
          int count =0;
          while(q!=0){
              q = q&(q-1);
              count++;
          }
          if(count<=k)ans++;
      }
      System.out.println(ans);
    }
}