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 main():

        txt = input()
        txt = txt.split()
        a = float(txt[0])
        b = float(txt[1])
        c = float(txt[2])
        d = float(txt[3])

        x = a/b
        y = c/d

        q = (1-x)*(1-y)

        p = x/(1-q)

        print(f'{p:.10}')
if __name__ == '__main__':
    main()