10566: ABC121 —— D - XOR World
[Creator : ]
Description
Let $f(A, B)$ be the exclusive OR of $A, A+1, ..., B$. Find $f(A, B)$.
What is exclusive OR?
The bitwise exclusive OR of integers $c_1, c_2, ..., c_n$ (let us call it $y$) is defined as follows:
- When $y$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if, the number of integers among $c_1, c_2, ...c_m$ whose binary representations have $1$ in the $2^k$'s place, is odd, and $0$ if that count is even.
For example, the exclusive OR of $3$ and $5$ is $6$. (When written in base two: the exclusive OR of `011` and `101` is `110`.)
What is exclusive OR?
The bitwise exclusive OR of integers $c_1, c_2, ..., c_n$ (let us call it $y$) is defined as follows:
- When $y$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if, the number of integers among $c_1, c_2, ...c_m$ whose binary representations have $1$ in the $2^k$'s place, is odd, and $0$ if that count is even.
For example, the exclusive OR of $3$ and $5$ is $6$. (When written in base two: the exclusive OR of `011` and `101` is `110`.)
Input
Input is given from Standard Input in the following format:
```
$A$ $B$
```
```
$A$ $B$
```
Output
Compute $f(A, B)$ and print it.
Constraints
- All values in input are integers.
- $0 \leq A \leq B \leq 10^{12}$
- $0 \leq A \leq B \leq 10^{12}$
Sample 1 Input
2 4
Sample 1 Output
5
2,3,4 are 010, 011, 100 in base two, respectively. The exclusive OR of these is 101, which is 5 in base ten.
Sample 2 Input
123 456
Sample 2 Output
435
Sample 3 Input
123456789012 123456789012
Sample 3 Output
123456789012