Problem:
Score : 100 points

Problem Statement

We have N+M balls, each of which has an integer written on it.

It is known that:

The numbers written on N of the balls are even.

The numbers written on M of the balls are odd.

Find the number of ways to choose two of the N+M balls (disregarding order) so that the sum of the numbers written on them is even.

It can be shown that this count does not depend on the actual values written on the balls.

Constraints

0 \leq N,M \leq 100

2 \leq N+M

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the answer.

Sample Input 1

2 1

Sample Output 1

1

For example, let us assume that the numbers written on the three balls are 1,2,4.

If we choose the two balls with 1 and 2, the sum is odd;

If we choose the two balls with 1 and 4, the sum is odd;

If we choose the two balls with 2 and 4, the sum is even.

Thus, the answer is 1.

Sample Input 2

4 3

Sample Output 2

9

Sample Input 3

1 1

Sample Output 3

0

Sample Input 4

13 3

Sample Output 4

81

Sample Input 5

0 3

Sample Output 5

3

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
using static System.Math;
using System.Linq;
using static System.Array;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            var NK = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
            var N = NK[0];
            var K = NK[1];

            
            Console.WriteLine((N*(N-1)+K*(K-1))/2);
        }

        

    }

    class Modular
    {
        private const int M = 1000000007;
        public long value;
        public Modular(long value) { this.value = value; }
        public static implicit operator Modular(long a)
        {
            var m = a % M;
            return new Modular((m < 0) ? m + M : m);
        }
        public static Modular operator +(Modular a, Modular b)
        {
            return (a.value + b.value) % M;
        }
        public static Modular operator -(Modular a, Modular b)
        {
            return a.value - b.value;
        }
        public static Modular operator *(Modular a, Modular b)
        {
            return a.value * b.value;
        }
        public static Modular Pow(Modular a, int n)
        {
            switch (n)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular operator /(Modular a, Modular b)
        {
            return a * Pow(b, M - 2);
        }
        private static readonly List<int> facs = new List<int> { 1 };
        private static Modular Fac(int n)
        {
            for (int i = facs.Count; i <= n; ++i)
            {
                facs.Add((int)(Math.BigMul(facs.Last(), i) % M));
            }
            return facs[n];
        }
        public static Modular Ncr(int n, int r)
        {
            return (n < r) ? 0
                 : (n == r) ? 1
                            : Fac(n) / (Fac(r) * Fac(n - r));
        }
        public static explicit operator int(Modular a)
        {
            return (int)a.value;
        }

        public static Modular Lcm(Modular a, Modular b)
        {
            var tmp = Gcdl(a.value, b.value);
            return ((a * b) / new Modular(tmp));
        }
        static Modular Gcd(Modular m, Modular n)
        {
            if (n.value > m.value) return Gcd(n, m);
            if (n.value == 0) return m;
            var r = new Modular(m.value % n.value);
            return Gcd(n, r);
        }

        static long Gcdl(long m, long n)
        {
            if (n > m) return Gcdl(n, m);
            if (n == 0) return m;
            return Gcdl(n, m % n);
        }
    }
}