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():
    inp = list(map(int, input().split()))
    a = inp[0]
    b = inp[1]
    c = inp[2]
    d = inp[3]
    prob_small_r_win = a/b
    prob_zanoes_win = c/d
    prob_both_lose = (1-prob_small_r_win)*(1-prob_zanoes_win)
    print(round(prob_small_r_win/(1-prob_both_lose), 12))

main()