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:
# URL: http://codeforces.com/problemset/problem/312/B

from typing import List


def parse_input() -> List[int]:
    return [int(x) for x in input().split()]


def solve(a: int, b: int, c: int, d: int) -> float:
    p = a/b
    q = c/d
    return p / (p + q - q*p)


if __name__ == '__main__':
    a, b, c, d = parse_input()
    print(solve(a, b, c, d))