Equivalent Resistance

In an electric circuit, when two resistors R_1 and R_2 are connected in parallel, the equivalent resistance R_3 can be derived from the following formula:

• \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_3}

Given R_1 and R_2, find R_3.

Constraints

• 1 \leq R_1, R_2 \leq 100
• R_1 and R_2 are integers.

Input

The input is given from Standard Input in the following format:

R_1 R_2

Output

Print the value of R_3.

The output is considered correct if the absolute or relative error is at most 10^{-6}.

Examples

Input

2 3

Output

1.2000000000

Input

100 99

Output

49.7487437186

inputFormat

Input

The input is given from Standard Input in the following format:

R_1 R_2

outputFormat

Output

Print the value of R_3.

The output is considered correct if the absolute or relative error is at most 10^{-6}.

Examples

Input

2 3

Output

1.2000000000

Input

100 99

Output

49.7487437186

样例

100 99

49.7487437186