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# CF912B New Year's Eve

• 28通过
• 50提交
• 题目来源
• 评测方式 RemoteJudge
• 标签 位运算,按位 贪心 进制
• 难度 普及-
• 时空限制 1000ms / 256MB
• 提示：收藏到任务计划后，可在首页查看。

## 题意翻译

题意：给定两个整数$n$ ,$k$ ,在$1$ ~$n$ 中选择至多$k$ 个整数，使得其异或和最大。求解这个最大值。

感谢@char32_t 提供的翻译

## 题目描述

Since Grisha behaved well last year, at New Year's Eve he was visited by Ded Moroz who brought an enormous bag of gifts with him! The bag contains $n$ sweet candies from the good ol' bakery, each labeled from $1$ to $n$ corresponding to its tastiness. No two candies have the same tastiness.

The choice of candies has a direct effect on Grisha's happiness. One can assume that he should take the tastiest ones — but no, the holiday magic turns things upside down. It is the xor-sum of tastinesses that matters, not the ordinary sum!

A xor-sum of a sequence of integers $a_{1},a_{2},...,a_{m}$ is defined as the bitwise XOR of all its elements: , here denotes the bitwise XOR operation; more about bitwise XOR can be found here.

Ded Moroz warned Grisha he has more houses to visit, so Grisha can take no more than $k$ candies from the bag. Help Grisha determine the largest xor-sum (largest xor-sum means maximum happiness!) he can obtain.

## 输入输出格式

输入格式：

The sole string contains two integers $n$ and $k$ ( $1<=k<=n<=10^{18}$ ).

输出格式：

Output one number — the largest possible xor-sum.

输入样例#1： 复制
4 3

输出样例#1： 复制
7

输入样例#2： 复制
6 6

输出样例#2： 复制
7

## 说明

In the first sample case, one optimal answer is $1$ , $2$ and $4$ , giving the xor-sum of $7$ .

In the second sample case, one can, for example, take all six candies and obtain the xor-sum of $7$ .

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