Random Teams

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 2people, maximum number can be achieved if participants were split on teams of 1, 1 and 4 people.

其实题目可以转化为

A1+A2+...+An=n;

求C(A1,2)+C(A2,2)+C(A3,2)+...+C(An,2)的最大最小值

利用高中学过的基本不等式就可以了

其实 好像用常识就可以解题了，，，我认为。。。

#include<iostream>
using namespace std;
long long int fun(long long int i){
    if(i<2)return 0;
    if(i%2==1)return (i-1)/2*i;
    return i/2*(i-1);
}
int main(){
    long long int n,m;
    while(cin>>n>>m){
        long long int t=n/m;
        long long int t1=n%m;
        long long int mi;
        mi=fun(t+1)*t1+fun(t)*(m-t1);
       long long int ma=fun(n-m+1);
        cout<<mi<<" "<<ma<<endl;
    }
return 0;
}