#### 464. Optimal bribing

Time limit per test: 0.5 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard

It is not easy to live and do business in Russia. For example, to get approval for gas utilities installation according to Russian law you need to get project documentation from city project bureau. But to get project documentation you will be required to get approval for gas utilities installation. Even to people who don't write computer programs and don't know buzz words like "endless recursion" it is clear that to get access to gas one needs to make a wonder. For example, to give bribe or kickback.

Suppose that every businessman acts optimally to maximize expected difference between profit and costs (which is the total sum of bribes paid), knowing the strategy of another player. What is the probability to win the project for each of them?

Input
Input file contains numbers N, F1, F2, V from the problem statement. N and V are integers, F1 and F2 are given with not more than two digits after decimal point (1 ≤ N ≤ 10, 0 < F1, F2 < 1, 1 ≤ V ≤ 100). Numbers will be chosen so that businessmen will have unique equilibrium combination of optimal bribing strategies (so, required probabilities will be unique as well).

Output
Write to the output file required probabilities with accuracy not less than 10-6.

Example(s)
 `sample input` `sample output` ```1 0.14 0.10 20 ``` ```0.618627007 0.381372993 ```