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 get_f_win_chance(f_num, f_denom, s_num, s_denom):
    f_hit_ch = f_num / f_denom
    s_hit_ch = s_num / s_denom
    f_win_ch = 0
    prob_remainder = 1
    while prob_remainder > 10 ** (-8):
        f_this_hit_win_ch = f_hit_ch * prob_remainder
        prob_remainder -= f_this_hit_win_ch
        f_win_ch += f_this_hit_win_ch

        s_this_hit_win_ch = s_hit_ch * prob_remainder
        prob_remainder -= s_this_hit_win_ch
    return f_win_ch


if __name__ == '__main__':
    f_num, f_denom, s_num, s_denom = (int(x) for x in input().split())
    print(get_f_win_chance(f_num, f_denom, s_num, s_denom))