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/env python
# -*- coding: utf-8 -*-
# @Date    : 2015-06-03 21:32:26
# @Author  : Your Name (you@example.org)
# @Link    : http://example.org
# @Version : $Id$

a=[]
for x in raw_input().split(" "):
	a.append(float(x))
a1=a[0]
b=a[1]
c=a[2]
d=a[3]
print (a1/b/(1-(1-a1/b)*(1-c/d)))