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 . 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.