Password

你有 $n$ 个灯泡，一开始都未点亮。 同时你有 $l$ 个长度，分别为 $a_1 \sim a_l$。 每次你可以选择一段连续的子序列，且长度为某个 $a_i$，并将这些灯泡的明灭状态取反。 求最少的操作次数，使得最后有且仅有 $k$ 个位置是亮的，这些位置已经给定，为 $x_1 \sim x_k$。

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.

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}&lt;x_{2}&lt;...&lt;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.

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

10 8 2
1 2 3 5 6 7 8 9
3 5

2

3 2 1
1 2
3

-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.