New Year's Eve

1000ms

262144K

Description:

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, ..., a_m is defined as the bitwise XOR of all its elements: $\text{[math]}$ , here $\text{[math]}$ 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.

Input:

The sole string contains two integers n and k (1 ≤ k ≤ n ≤ 10¹⁸).

Output:

Output one number — the largest possible xor-sum.

Sample Input:

4 3

Sample Output:

Sample Input:

6 6

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF912B