Codeforces 467B Fedor and New Game

B. Fedor and New Game

time limit per test

1 second

memory limit per test

256 megabytes

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

7 3 18511117

output

0

input

3 3 31234

output

3

题目大意：有 m + 1 个 player 和 n 种类型的 soldiers。每个player被赋予一个数xi，然后将xi 看成二进制数，规定第 j 位 如果为1，表示这个 player 有j 这种类型的soldiers。Fedor 是 第 m + 1 个player，问他能跟前面 m 个players 成为 friends 的人数。成为friends 的条件是被比较的两个人的不同soldiers数不得多于 k 个（两个二进制数对应位相等的个数小于等于k）。

参考别人的代码:

#include<iostream>#include<algorithm>using namespace std;const int maxn = 1005;int a[maxn];int bit(int x){return x == 0 ? 0 : bit(x >> 1) + (x & 1);}int main(){int n,m,k;while (cin >> n >> m >> k){int i, ans = 0;for (i = 0; i <= m; i++)cin >> a[i];for (i = 0; i < m; i++){if (bit(a[i] ^ a[m]) <= k)ans ++ ;}cout << ans << endl;}return 0;}