Count the Length

Time Limit: 2 Seconds
Memory Limit: 65536 KB
Special Judge

You are given a board of `m*n`, so there are `m*n` unit squares(1*1) in the board. Suppose all unit squares are colored red or blue, and no adjacent(have common edge) unit squares share the same color. Consider the diagonal `D` of the board from left bottom to right top, `D` is a segment with color too, a point in `D` is red(or blue) if it falls in a red(or blue) unit square. Assume the left bottom square's color is red, then what is the total length of red part of the diagonal `D`?

the sample of 2 * 4 board

the total length of red part of the diagonal is 2.236068

#### Input

There are multiple test cases(less than 10000).
Each case is a line containing two integers `m,n`(1 ≤ `m,n` ≤ 2^31-1).

#### Output

For each case, output a single line containing the right answer(rounded up to 3 digits after the decimal point).

#### Sample Input

2 4
1 3

#### Sample Output

2.236
2.108

Author:

**ZHANG, Debing**
Contest:

**ZOJ Monthly, February 2012**
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