Algorithm

B. Fedor and New Game
time limit per test
1 second
memory limit per test
256 megabytes
problem link- https://codeforces.com/problemset/problem/467/B
input
standard input
output
standard output

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
Copy
7 3 1
8
5
111
17
output
Copy
0
input
Copy
3 3 3
1
2
3
4
output
Copy
3



 

Code Examples

#1 Code Example with C++ Programming

Code - C++ Programming

#include <bits/stdc++.h>

using namespace std;

int diff(int a, int b) {
  bitset<32> aa(a), bb(b);
  int res = 0;
  for(int i = 0; i < 32; ++i)
    res += (aa[i] != bb[i]);
  return res;
}

int main() {
  int n, m, k, f;
  scanf("%d %d %d", &n, &m, &k);
  int a[1001];
  for(int i = 0; i < m; ++i)
    scanf("%d", a + i);
  scanf("%d", &f);
  
  int res = 0;
  for(int i = 0; i < m; ++i) {
    int d = diff(a[i], f);
    if(d <= k)
      ++res;
  }
  printf("%d\n", res);
  
  return 0;
}
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Input

x
–
+
cmd
7 3 1
8
5
111
17
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Demonstration

Codeforces Solution-Fedor and New Game-Solution in C, C++, Java, Python

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