A8106 | 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.

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.

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