// n people were split into m teams (there is at least one person in each team).

// Then all members within each team shook hands.

// Write a program that inputs n and m (0<m≤n) and 

// prints minimum and maximum number of possible handshakes.

using System;

using System.Diagnostics;

public class Program

{

    public static int InputInt(string prompt)

    {

        Console.Write("Enter " + prompt + ":");

        return Convert.ToInt32(Console.ReadLine());

    }

    public static void Main(string[] args)

    {

        // input

        int n = InputInt("number of people");

        int m = InputInt("number of teams");

        Trace.Assert(0 < m && m <= n);

        // maximum: m-1 single person groups plus 1 big group of n - m + 1 persons

        int maxHandShakes = (n-m+1)*(n-m)/2;

        // minimum: split to "almost" equal groups

        int smallTeamSize = n / m;

        int bigTeamSize = smallTeamSize + 1;

        int bigTeamCount = n - smallTeamSize * m; // same as  = n % m

        int smallTeamCount = m - bigTeamCount;

        /* n == smallTeamCount*smallTeamSize + bigTeamCount*bigTeamSize */

        int minHandShakes = smallTeamCount * smallTeamSize * (smallTeamSize - 1) / 2 + 

                              bigTeamCount * bigTeamSize   * (bigTeamSize   - 1) / 2;

        // output

        Console.WriteLine("Max Handshakes = " + maxHandShakes);

        Console.WriteLine("Min Handshakes = " + minHandShakes);

    }

}

​

​