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 a/b for SmallR while 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.

中文翻译:小R是个射手,正在与ZGX比赛。他们轮流射击,小R先手。每次射击,小R中靶的概率为a/b,ZGX中靶的概率为c/d。当有人中靶时,比赛立即结束,中靶者获胜。求小R获胜的概率。

Input
A single line contains four integers a,b,c,d (1<=a,b,c,d<=1000, 0<a/b<1, 0<c/d<1).

Output
Print a single real number, the probability that SmallR will win the match.
本题无SPJ,答案四舍五入保留12位小数。The answer will be considered correct if the absolute or relative error doesn't exceed 1e-6.

Sample test(s)
Input
1 2 1 2

Output
0.666666666667