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 PYTHON):

Solution:
import sys;

def main():
	inp=map(int,raw_input().split(" ",4))
	a=inp[0];b=inp[1];
	c=inp[2];d=inp[3];
	x=(b-a)*(d-c);
	x=float(x)/b;
	x=x/d;
	v=1/(1-x);
	ans=(float(a)*v)/b;
	print ans;
main()