Problem Description

Input Format

Inputs will be given by standard input in the following format:

$ H $ $ W $

• At the first line, $H(1≦H≦1,000,000,000),\ W(1≦W≦1,000,000,000)$, will be given separated by a space.

Output Format

Please calculate the maximum value that can be obtained, then output it in one line.

Print a newline at the end of the output.

Sample Input and Output

Sample Input #1

4 5

Sample Output #1

31

Sample Input #2

314159265 358979323

Sample Output #2

144115188075855871

Notes/Hints

Problem

Cat Snuke received a paper that has been divided into grids having $ H $ horizontal rows and $ W $ vertical columns as a birthday gift. For each block, a number is written as shown in the figure below.

More precisely, the number, which is written in the $ i_{th} $ row from the top of the rectangle paper and $ j_{th} $ column from the left of the rectangle paper, is $(i\ -\ 1)\ \times\ W\ +\ (j\ -\ 1)$.

Cat Snuke wants to choose a partial rectangle from this rectangle paper, then find the value obtained by bitwise $ xor $ for all the numbers in this partial rectangle. Specifically, Cat Snuke will choose integers $ t,b(1≦t≦b≦H),l,r(1≦l≦r≦W) $, then calculate the value obtained by bitwise $ xor $ for all the numbers in the area from the top of the rectangle between the $ t_{th} $ row and the $ b_{th} $ row (including both ends), from the left of the rectangle between the $ l_{th} $ column and $ r_{th} $ column (including both ends).

Cat Snuke is able to choose any values for $ t,b,l,r $. Please calculate the maximum value that can be obtained.

Sample Explanation 1

For example, the obtained value of $ t=3,b=4,l=3,r=5 $ is $12\ xor\ 13\ xor\ 14\ xor\ 17\ xor\ 18\ xor\ 19\ =\ 31$, this is the maximum value that can be obtained in this case.

见题面 Input 部分

见题面 Output 部分