D - XOR World

Score : $400$ points

Problem Statement

Let $f(A, B)$ be the exclusive OR of $A, A+1, ..., B$. Find $f(A, B)$.

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.)

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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.

2 4

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.

123 456

435

123456789012 123456789012

123456789012