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:
'''                      
   	
   			 ||Sri:||                 

                      __|
 ______________|_________________________
      |    |   ___|    |    |    ___|      |      |    |___
 /\  /\    |   |___    |    |   |___|      |      |    |___|
/  \/  \   |   ___|    |    |         |_/    |___|    |___

I am a beginner. Feel free to send tutorials/help to srinivasan1995@gmail.com.

Codeforces, SPOJ handle: desikachariar.
Hackerrank, Codechef handle: Prof_Calculus.

Advices/Help are welcome. You will definitely get a thanks in return. Comments to be avoided.

College: International Institute of Information Technology, Bangalore.

'''

import math

if __name__ == '__main__':
	a,b,c,d= [float(pp) for pp in raw_input().split(' ')]
	print float(a/b)/(1.00000 - ((1.0000 - float(a/b))*(1.0000 - float(c/d))))