CF467B.Fedor and New Game

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 x__i. Consider binary representation of x__i: if the j-th bit of number x__i 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.

在你帮助乔治和亚历克斯搬进宿舍后，他们去帮朋友费多尔玩一款新的电脑游戏《士兵召唤3》。

该游戏共有 $m+1$ 名玩家和 $n$ 种士兵类型。《士兵召唤3》的玩家编号为 $1$ 到 $m+1$；士兵类型编号为 $0$ 到 $n-1$。每名玩家都拥有一支军队。第 $i$ 名玩家的军队可用一个非负整数 $x_i$ 表示：考察 $x_i$ 的二进制表示，若 $x_i$ 的第 $j$ 位（从低位起，即最低位为第 $0$ 位）为 $1$，则表明该玩家的军队中包含第 $j$ 种类型的士兵。

费多尔是该游戏的第 $(m+1)$ 名玩家。他认为：若两名玩家的军队在至多 $k$ 种士兵类型上存在差异（即对应数字的二进制表示至多有 $k$ 个比特位不同），则这两名玩家可以成为朋友。请帮助费多尔计算他能与多少名玩家成为朋友。

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 x__i (1 ≤ x__i ≤ 2_n_ - 1), that describes the i-th player's army. We remind you that Fedor is the (m + 1)-th player.

第一行包含三个整数 $n$、$m$、$k$（$1 \le k \le n \le 20$；$1 \le m \le 1000$）。

接下来的 $m+1$ 行中，第 $i$ 行包含一个整数 $x_i$（$1 \le x_i \le 2^n - 1$），用于描述第 $i$ 位玩家的军队。我们提醒您：费多尔是第 $m+1$ 位玩家。

Print a single integer — the number of Fedor's potential friends.

输出一个整数——费多尔潜在朋友的数量。