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;
void printvictor(vector<long long> v) {
  for (long long i = 0; i < v.size(); i++) cout << v[i] << " ";
  cout << endl;
}
template <class T>
string toStr(const T &x) {
  stringstream s;
  s << x;
  return s.str();
}
template <class T>
int toInt(const T &x) {
  stringstream s;
  s << x;
  int r;
  s >> r;
  return r;
}
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
bool isprime(long long n) {
  if (n == 2) return true;
  if (n < 2 || n % 2 == 0) return false;
  for (long long i = 3; i * i <= n; i += 2) {
    if (n % i == 0) return false;
  }
  return true;
}
int main() {
  long long n = 0, f, S, B, L, R, c = 0, d = 0, hs, hu, m = 0, l1 = 0, l2, l3,
            l4, y = 0, r = 0, k = 0, i = 0, pos1 = 0, pointer = 1, pos2 = 0,
            j = 0, sum1 = 0, low = 0, high = 1000000000, counter = 0,
            counter2 = 0, counter3 = 0, temp1, temp2, flag2 = 0, flag1 = 0,
            sum = 0;
  cin >> n >> m >> k;
  vector<long long> numbers(m + 1);
  vector<string> bitsets(m + 1);
  for (long long i = 0; i < m + 1; i++) cin >> numbers[i];
  for (long long i = 0; i < numbers.size(); i++) {
    bitset<32> x(numbers[i]);
    bitsets[i] = x.to_string();
  }
  string s = bitsets[bitsets.size() - 1];
  for (long long i = 0; i < bitsets.size(); i++) {
    temp1 = i;
    temp2 = k;
    if (i != bitsets.size() - 1) {
      for (long long i = 0; i < bitsets[temp1].length(); i++) {
        if (bitsets[temp1][i] != s[i]) temp2--;
      }
      if (temp2 >= 0) counter++;
    }
  }
  cout << counter << endl;
  return 0;
}