Polygons

Description:

Input:

The only line of input contains two integers $$$n$$$ and $$$k$$$ ($$$3 \le n \le 10^{6}$$$, $$$1 \le k \le n-2$$$), the maximum number of sides of a polygon and the number of polygons to construct, respectively.

Output:

Print a single integer — the minimum number of points required for $$$k$$$ polygons.

Sample Input:

6 2

Sample Output:

6

Sample Input:

200 50

Sample Output:

708

Note:

In the first example, we have $$$n = 6$$$ and $$$k = 2$$$. So, we have $$$4$$$ polygons with number of sides $$$3$$$, $$$4$$$, $$$5$$$ and $$$6$$$ to choose from and if we choose the triangle and the hexagon, then we can arrange them as shown in the picture in the statement.

Hence, the minimum number of points required on the circle is $$$6$$$, which is also the minimum overall possible sets.