XOR World

题目描述

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 $110$.)

输入格式

Input is given from Standard Input in the following format: $A$ $B$

输出格式

Compute $f(A, B)$ and print it.

2 4

5

123 456

435

123456789012 123456789012

123456789012

提示

All values in input are integers. $0 \leq A \leq B \leq 10^{12}$$2, 3, 4$ are $010$, $011$, $100$ in base two, respectively. The exclusive OR of these is $101$, which is $5$ in base ten.

标签: AtCoder|abc121D

来源

AtCoder|abc121D