101213: [AtCoder]ABC121 D - XOR World
Memory Limit：256 MB
Time Limit：2 S
Judge Style：Text Compare
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Submit：0
Solved：0
Description
Score : $400$ points
Problem Statement
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.)
Constraints
- All values in input are integers.
- $0 \leq A \leq B \leq 10^{12}$
Input
Input is given from Standard Input in the following format:
$A$ $B$
Output
Compute $f(A, B)$ and print it.
Sample Input 1
2 4
Sample Output 1
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 Input 2
123 456
Sample Output 2
435
Sample Input 3
123456789012 123456789012
Sample Output 3
123456789012