Play the Dice

Time Limit: 2000 MS

Memory Limit: 65535 MB

Description

There is a dice with N sides, which are numbered from 1,2,...,n and have the equal possibility to show up when one rolls a dice. Each side has an integer Ai on it. Now here is a game that you can roll this dice once, if the i-th side is up, you will get Ai yuan. What's more, some sids of this dice are colored with a special different color. If you turn this side up, you will get once more chance to roll the dice. When you roll the dice for the second time, you still have the opportunity to win money and rolling chance. Now you need to calculate the expectations of money that we get after playing the game once.

Input

Input consists of multiple cases. Each case includes two lines. End with EOF.
The first line is an integer N (2<=N<=200), following with N integers Ai(0<=Ai<200)
The second line is an integer M (0<=M<=N), following with m integers Bi(1<=Bi<=n), which are the numbers of the special sides to get another more chance.

Output

Just a real number which is the expectations of the money one can get, rounded to exact two digits. If you can get unlimited money, print "inf" a line without double quotes.

Sample Input

6 1 2 3 4 5 6
0
4 0 0 0 0
1 3

Sample Output

3.50
0.00

Hint

None

Source

2013 ACM-ICPC China Nanjing Invitational Prog

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