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 random
s = raw_input().split()

r = float(s[0])/int(s[1])
z = float(s[2])/int(s[3])

num_sim = 20000
v = 0.0
for i in range(num_sim):
    c1 = ((1-r)**i)*((1-z)**i)*r
    v = v+ c1


print v