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:
def archer(a,b,c,d):
    loss1=(1-(a/b))
    loss2=(1-(c/d))
    win1=a/b
    return win1*(1/(1-(loss1*loss2)))


a,b,c,d=map(int,input().strip().split())
print(archer(a,b,c,d))