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.

Input

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.

Output

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

Print a newline at the end of output.

Input Example 1

4 5

Output Example 1

31
```![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.

* * *

### Input Example 2

```plain

314159265 358979323

Output Example 2

144115188075855871