Problem: 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 <image> for SmallR while <image> 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 <image>.

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

Solution (in PYTHON3):

Solution:
import math
inp = lambda cast=int: [cast(x) for x in input().split()]
printf = lambda s='', *args, **kwargs: print(str(s).format(*args), flush=True, **kwargs)

a, b, c, d = inp()
nr, dr = a*d, b*d - (b-a)*(d-c)
printf('{:.12f}', nr/dr)