CF79D.Password

Finally Fox Ciel arrived in front of her castle!

She have to type a password to enter her castle. An input device attached to her castle is a bit unusual.

The input device is a 1 × n rectangle divided into n square panels. They are numbered 1 to n from left to right. Each panel has a state either ON or OFF. Initially all panels are in the OFF state. She can enter her castle if and only if _x_1-th, _x_2-th, ..., x__k-th panels are in the ON state and other panels are in the OFF state.

She is given an array _a_1, ..., a__l. In each move, she can perform the following operation: choose an index i (1 ≤ i ≤ l), choose consecutive a__i panels, and flip the states of those panels (i.e. ON → OFF, OFF → ON).

Unfortunately she forgets how to type the password with only above operations. Determine the minimal number of operations required to enter her castle.

最终，小狐狸雪儿抵达了她的城堡前！

她需要输入密码才能进入城堡。连接在城堡上的输入设备有些特别。

该输入设备是一个 $1 \times n$ 的矩形，被划分为 $n$ 个正方形面板，从左到右编号为 $1$ 到 $n$。每个面板的状态为“开（ON）”或“关（OFF）”。初始时所有面板均为“关（OFF）”状态。当且仅当第 $x_1$、$x_2$、…、$x_k$ 个面板处于“开（ON）”状态，而其余面板均处于“关（OFF）”状态时，她才能进入城堡。

她被给定一个数组 $a_1, \dots, a_l$。在每次操作中，她可以执行以下操作：选择一个下标 $i$（满足 $1 \le i \le l$），再选择一段连续的 $a_i$ 个面板，并翻转这些面板的状态（即 ON → OFF，OFF → ON）。

不幸的是，她忘记了仅用上述操作输入密码的方法。请确定进入城堡所需的最少操作次数。

The first line contains three integers n, k and l (1 ≤ n ≤ 10000, 1 ≤ k ≤ 10, 1 ≤ l ≤ 100), separated by single spaces.

The second line contains k integers _x_1, ..., x__k (1 ≤ _x_1 < _x_2 < ... < x__k ≤ n), separated by single spaces.

The third line contains l integers _a_1, ..., a__l (1 ≤ a__i ≤ n), separated by single spaces. It is possible that some elements of the array a__i are equal value.

第一行包含三个整数 $n$、$k$ 和 $l$（$1 ≤ n ≤ 10000$，$1 ≤ k ≤ 10$，$1 ≤ l ≤ 100$），以单个空格分隔。

第二行包含 $k$ 个整数 $x_1, \dots, x_k$（$1 ≤ x_1 < x_2 < \dots < x_k ≤ n$），以单个空格分隔。

第三行包含 $l$ 个整数 $a_1, \dots, a_l$（$1 ≤ a_i ≤ n$），以单个空格分隔。数组 $a_i$ 中的某些元素可能取值相等。

Print the minimal number of moves required to type the password. If it's impossible, print -1.

输出输入密码所需的最少移动次数。如果无法输入，则输出 $-1$。

One possible way to type the password in the first example is following: In the first move, choose 1st, 2nd, 3rd panels and flip those panels. In the second move, choose 5th, 6th, 7th, 8th, 9th panels and flip those panels.

第一个示例中输入密码的一种可能方式如下：在第一次操作中，选择第 1、第 2 和第 3 个面板并翻转这些面板；在第二次操作中，选择第 5、第 6、第 7、第 8 和第 9 个面板并翻转这些面板。