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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int xx[4] = {0, 0, 1, -1};
int yy[4] = {1, -1, 0, 0};
int n, m, k, s;
int a[int(1e5)];
int getbit(int x, int i) { return (x >> i) & 1; }
int main() {
  scanf("%d%d%d", &n, &m, &k);
  for (int i = (1), _b = (m); i <= _b; i++) {
    scanf("%d", &a[i]);
  }
  scanf("%d", &s);
  int res = 0;
  for (int i = (1), _b = (m); i <= _b; i++) {
    int dem = 0;
    for (int x = (0), _b = (n - 1); x <= _b; x++)
      if (getbit(s, x) != getbit(a[i], x)) {
        dem++;
      }
    if (dem <= k) res++;
  }
  cout << res << endl;
}