Recently,  became obsessed with a fighting game. In this game,  characters stand on an arena from left to right, and the combat power of the  character is . For each operation,  will choose two adjacent characters  and  on the arena for a duel. If , then  wins, if , then  wins. If , then both  and  have a probability of  to win. The victorious character will stay in the arena and double the combat power; the losing character will leave the arena.

Now will perform  operations, after  operations, there will only be one character left in the ring. Obviously,  has  operation modes. In all these modes of operation, which characters have the probability to stay till the end and become the final winner.

The first line contains a positive integer , which represents the number of the characters.

The second line contains  integers separated by spaces , which represents the the combat power of the  character.

The first line contains a positive integer , which represents the number of the characters who have the probability to stay till the end and become the final winner.

The second line contains  integers in  order separated by spaces , which represents the the index of the characters who have the probability to stay till the end and become the final winner.

3
1 2 3

2
2 3

3
2 2 4

3
1 2 3

5
1 2 30 16 1

2
3 4