AT_code_festival_2015_okinawa_e Enormous XOR Rectangle

[problemUrl]: https://atcoder.jp/contests/code-festival-2015-okinawa-open/tasks/code_festival_2015_okinawa_e

Inputs will be given by standard input in 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 divided by space.

Please calculate the maximum value that can be obtained, then output it in one line. Print a newline at the end of output.

### 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), form 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 !\[sample\](https://code-festival-2015-okinawa.contest.atcoder.jp/img/other/code\_festival\_2015\_okinawa/vfgagrt/E2.png)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.