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:
inp = input().split()
a = int(inp[0])
b = int(inp[1])
c = int(inp[2])
d = int(inp[3])
Rwin = a/b
Rlose = 1-Rwin
Zlose = 1-(c/d)
print( '%.7f' % (Rwin/(1-(Rlose*Zlose))) )