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;
vector<long long> x;
int main() {
  int n, m, k;
  cin >> n >> m >> k;
  x.assign(m, 0);
  for (int i = 0; i < m; ++i) {
    cin >> x[i];
  }
  int xf;
  cin >> xf;
  for (int i = 0; i < m; ++i) {
    x[i] = xf ^ x[i];
  }
  long long sd;
  int cnt, ans = 0;
  for (int i = 0; i < m; ++i) {
    cnt = 0;
    sd = 1;
    for (int j = 0; j < n; ++j) {
      if ((x[i] & sd) == sd) {
        cnt++;
      }
      sd *= 2;
    }
    if (cnt <= k) ans++;
  }
  cout << ans;
  return 0;
}