Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Random Teams

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard output*n* participants of the competition were split into *m* teams in some manner so that each team has at least one participant. After the competition each pair of participants from the same team became friends.

Your task is to write a program that will find the minimum and the maximum number of pairs of friends that could have formed by the end of the competition.

Input

The only line of input contains two integers *n* and *m*, separated by a single space (1 ≤ *m* ≤ *n* ≤ 10^{9}) — the number of participants and the number of teams respectively.

Output

The only line of the output should contain two integers *k*_{min} and *k*_{max} — the minimum possible number of pairs of friends and the maximum possible number of pairs of friends respectively.

Examples

Input

5 1

Output

10 10

Input

3 2

Output

1 1

Input

6 3

Output

3 6

Note

In the first sample all the participants get into one team, so there will be exactly ten pairs of friends.

In the second sample at any possible arrangement one team will always have two participants and the other team will always have one participant. Thus, the number of pairs of friends will always be equal to one.

In the third sample minimum number of newly formed friendships can be achieved if participants were split on teams consisting of 2 people, maximum number can be achieved if participants were split on teams of 1, 1 and 4 people.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/08/2021 07:31:53 (g1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|