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:
a,b,c,d = map(int,raw_input().split());

p = a*1.0/b;
q = c*1.0/d;

ans = 0.0;
tot = 1.0;
while True:
	if tot * p < 1e-15:
		break;
	ans += tot * p;
	tot *= (1 - p)*(1 - q);
print ans;