CF912B.New Year's Eve
普及/提高-
通过率:0%
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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 a1,a2,...,am 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.
输入格式
The sole string contains two integers n and k ( 1<=k<=n<=1018 ).
输出格式
Output one number — the largest possible xor-sum.
输入输出样例
输入#1
4 3
输出#1
7
输入#2
6 6
输出#2
7
说明/提示
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 .