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:
import sys
a,b,c,d=map(int,input().split())
s=0;p=1;i=1
while True:
    if i%2:
        s+=p*a/b
        p*=(1-a/b)
    else:
        p*=(1-c/d)
    if p<1e-7:
        print(round(s,6))
        sys.exit()
    i=i+1