In a casino, there is a bag with $a$ white balls and $b$ black balls. Until the bag is empty, we can pick one ball randomly from the bag, and if it is white, we gain $1$ dollar; otherwise, we lose $1$ dollar. After that, we trash this ball. We can stop at any time, including the time before picking any balls. What maximum expected profit can we get?

Input

The input contains two space-separated integers, $a$ and $b$ ($0 \le a, b \le 100\,000$).

Output

Print one real number: the maximum expected profit. The answer will be considered correct if the absolute or relative error is at most $10^{-6}$.

Examples

Sample Input 1

0 0

Sample Output 1

0

Sample Input 2

3 4

Sample Output 2

0.342857142857142857

Sample Input 3

2 2

Sample Output 3

0.666666666666666666

Sample Input 4

3 0

Sample Output 4

3

Note

Don't forget setprecision if you use C++.