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:
entrada = input()
itens = entrada.split()
a, b, c, d = float(itens[0]), int(itens[1]), int(itens[2]), int(itens[3])

prob_win_sr = a/b
prob_win_zn = c/d

prob_failure = (1-prob_win_sr) * (1-prob_win_zn)

result = prob_win_sr/(1-prob_failure)

print(result)