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 PYTHON):

Solution:
'''
Created on 2013-5-26

@author: zhxfl
'''
a, b , c, d = map(float, raw_input().split());
ans = a / b
win = a / b;
lost = 1.0;
while 1:
    if c == d:
        break;
    if ans == 1.0:
        break;
    lost *= (1.0 - a / b) * (1.0 - c / d);
    ans += a / b * lost;
    if lost <= 0.000000001 or ans == 1.0:
        break;
print ans;