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
