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:
# n = int (input())
# pointx,pointy=[],[]
# for i in range(n):
#     x , y = map(int,input().split())
#     pointx.append(x)
#     pointy.append(y)
# ans = max(max(pointx)-min(pointx),max(pointy)-min(pointy))
# print(ans  * ans)
a ,b ,c, d = map(int ,input().split())
q = 1-(1-a/b)*(1-c/d)
print(a/b/q)