Team Building

The management of a large software company wants to run team building training for all $n$ employees. The training lasts two days. Each day, participants complete various tasks in teams of $k$ people. The number of employees is divisible by $k$, so each day forms exactly $n / k$ teams of $k$ people. On both days the teams can be arbitrary, and the grouping on the second day may be completely independent of the first day.

The organizers are now making the schedule that assigns people to teams on each day. One goal of the training is for employees to work in a team with many different people, so the assignment has a natural requirement: the number of pairs of people who share a team on both days must be as small as possible.

Distributing people this way is harder than it looks. Find the minimum number of pairs of employees who end up in the same team on both days.

The only line contains two integers $n$ and $k$ ($4 \leq n \leq 10^9$, $2 \leq k < n$, $n$ is divisible by $k$), the number of employees in the company and the team size on both days of the training.

Print the minimum number of pairs of employees who share a team on both days.

In the first sample, the people can be split on day one into (2, 4, 9), (1, 3, 8), (5, 6, 7), and on day two into (2, 5, 8), (3, 4, 7), (1, 6, 9). With this split, no pair of people shares a team on both days.

In the second sample, day one can be split into the teams (1, 3, 5, 7) and (2, 4, 6, 8), and day two into (1, 2, 7, 8) and (3, 4, 5, 6). Then four pairs (1 and 7, 2 and 8, 3 and 5, 4 and 6) share a team on both days. It can be shown that no better solution exists.