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:
##Ps = a/b + ((1-a/b)*(1-c/d))*(Ps)
## c/d + a/b - ac/bd
##Ps * (-1+c/d+1) = a/b
##
##Ps = a*d / b*c
a,b,c,d=map(int,input().split())

print(a/(b*(c/d + a/b - (a*c)/(b*d))))