CF912B.New Year's Eve

普及/提高-

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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 nn sweet candies from the good ol' bakery, each labeled from 11 to nn 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,...,ama_{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 kk 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 nn and kk ( 1<=k<=n<=10181<=k<=n<=10^{18} ).

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 11 , 22 and 44 , giving the xor-sum of 77 .

In the second sample case, one can, for example, take all six candies and obtain the xor-sum of 77 .

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