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 sys

def solve():
    a, b, c, d = sys.stdin.readline().split()
    a = int(a)
    b = int(b)
    c = int(c)
    d = int(d)

    ver1 = float(a)/b
    ver2 = float(c)/d

    return ver1/(ver1+(1-ver1)*ver2)


print solve()