e-olymp
Problems

Prime Soccer

Prime Soccer

You are watching a soccer match, and you wonder what the probability is that at least one of the two teams will score a prime number of goals. The game lasts 90 minutes, and to simplify the analysis, we will split the match into five-minute intervals. The first interval is the first five minutes, the second interval is the next five minutes, and so on. During each interval, there is a skillOfTeamA percent probability that first team will score a goal, and a skillOfTeamB percent probability that second team will score a goal. Assume that each team will score at most one goal within each interval. Find the probability that at least one team will have a prime number as its final score.

Input

Each line contains two integers skillOfTeamA and skillOfTeamB (0 ≤skillOfTeamA, skillOfTeamB≤ 100), describing the percent probability to score a goal for the first and the second team during the five minutes interval.

Output

For each test case print in a separate line the probability that at least one team will have a prime number as its final score. Print the probabilities with 4 digits after the decimal point.

Time limit 1 second
Memory limit 64 MiB
Input example #1
50 50
100 100
12 89
Output example #1
0.5266
0.0000
0.6772