Description

Miying has $n$ different kinds of paints, numbered from $1$ to $n$. Each kind of paint can be used at most once. When she starts a painting, she may choose any one paint to use.

After that, each time Miying chooses a paint $i$ to use such that, after using paint $i$, the $gcd$ (greatest common divisor) of the indices of all paints used so far is as large as possible, that is:

Let the set of indices of paints already used be $A$. If $\ \exists\ i,\ j\notin A,\ i,\ j\in [1,\ n],\ gcd(A,\ i)>gcd(A,\ j)$, then paint $j$ cannot be chosen.

If there are multiple paints that satisfy the condition, Miying may choose any one of them. After each paint is used, Miying gains a happiness value equal to the $gcd$ of the indices of all paints used so far.

Now Miying wants to draw a painting using $m$ kinds of paints. What is the maximum possible sum of happiness values she can obtain?

Input Format

A single line with two positive integers $n,\ m$, representing the number of kinds of paints and the number of paints Miying will use.

Output Format

Output one positive integer, the maximum happiness value Miying can obtain.

7 4

11

15 3

25

Hint

$1\le m\le n\le 10^7$.

Constraints

Sample Explanation

Sample 1: 6 3 5 2 is an optimal solution. The happiness values obtained each time are 6 3 1 1.

Sample 2: 15 10 5 is an optimal solution. The happiness values obtained each time are 15 5 5.

Translated by ChatGPT 5