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:
a, b, c, d = map(int, input().split(' '))

prob = 0
x = 0
v1 = (b-a) * (d-c) / (b * d)

while True:
    
    tmp =  pow(v1, x)
    tmp *= (a/b)
    
    if tmp < 1e-10:
        print(prob)
        break
        
    
    prob += tmp
    x += 1