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():
    a, b, c, d = [int(i) for i in input().split()]
    # (a/b) + (a/b)*(1 - a/b)(1 - c/d) + a(/b)(1- /a/b)(1 - c/d)
    # s = a1 / (1 - q)
    answer = (a / b) * 1 / (1 - (1 - a / b) * (1 - c / d))
    print(answer)


if __name__ == '__main__':
    main()