#15. Diamond,
Diamond
Diamond. in/. out/. cpp
[Problem description]
You have n boxes of "quantum states". Each box may contain some money or a diamond.
Now you know that if you open the I-th box, you can get the V I Vi money with the probability of P I 100 Pi100, and you can get a diamond with the probability of 1-P I 100 Pi100.
Now you want to know the probability that you just get k (0 ≤ k ≤ n) diamond and get more than or equal to m.
Please output n + 1 answer for 0 ≤ k ≤ n.
The answer is rounded to three decimal places.
[Input format]
The first line has two integers, n and m.
Next n rows, each line has two integers V I Vi and P I Pi.
[Output format]
The output contains n + 1 rows, indicating the answer with 0 ≤ k ≤ n.
[Example input]
2 3
2 50
3 50
[Sample output]
0.250
0.250
0.000
[Data scale and Conventions]
For 30% of data, n ≤ 10.
For 60% of the data, n ≤ 15
For 100% of the data, n ≤ 30, 1 ≤ P I Pi ≤ 99, 1 ≤ V I Vi ≤ 10 ^ 7, 1 ≤ m ≤ 10 ^ 7.
[Restrictions]
Time: 1 s
Memory: 256 MB