CF912B New Year's Eve

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    • 50提交
  • 题目来源 CodeForces 912B
  • 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

题解

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    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.

    输入输出样例

    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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