SmallR is an archer. SmallR is taking a match of archer with Zanoes. They try to shoot in the target in turns, and SmallR shoots first. The probability of shooting the target each time is $\frac{a}{b}$ for SmallR while $\frac{c}{d}$ for Zanoes. The one who shoots in the target first should be the winner.

Output the probability that SmallR will win the match.

-----Input-----

A single line contains four integers $a, b, c, d(1 \leq a, b, c, d \leq 1000,0 < \frac{a}{b} < 1,0 < \frac{c}{d} < 1)$.

-----Output-----

Print a single real number, the probability that SmallR will win the match.

The answer will be considered correct if the absolute or relative error doesn't exceed 10^{ - 6}.

-----Examples-----

Input 1 2 1 2

Output 0.666666666667