B. Random Teams

time limit per test

memory limit per test

input

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?≤?109) ? the number of participants and the number of teams respectively.

Output

The only line of the output should contain two integers kmin and kmax ? the minimum possible number of pairs of friends and the maximum possible number of pairs of friends respectively.

Sample test(s)

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.

解題思路：n個(gè)人，m個(gè)隊(duì)，只有在一個(gè)隊(duì)的人可以兩兩成為朋友，問能比完賽后，朋友的對(duì)數(shù)的最大值和最小值為多少。

很顯然，最大值的分法是有n-1個(gè)隊(duì)中只放一個(gè)人， 把剩下的人全放到剩下的那個(gè)隊(duì)。最少的分法是盡可能的均分n個(gè)人到m個(gè)隊(duì)。具體的朋友對(duì)數(shù)是簡(jiǎn)單的組合，k個(gè)人兩兩之間的朋友對(duì)數(shù)為 C（k,2） = k*(k-1)/2 .

AC代碼：

#include #include #include #include #include #include #include #include 

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