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:
#!/usr/bin/python

if __name__=="__main__":
	s=raw_input();
	s=s.split();
	for i in range(len(s)):
		s[i]=float(s[i]);
	ans=s[0]/s[1];
	t=(1-s[0]/s[1])*(1-s[2]/s[3]);
	print ans*(1/(1-t));