Problem:
Score : 400 points

Problem Statement

We have N+1 integers: 10^{100}, 10^{100}+1, ..., 10^{100}+N.

We will choose K or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo (10^9+7).

Constraints

1 \leq N \leq 2\times 10^5

1 \leq K \leq N+1

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of possible values of the sum, modulo (10^9+7).

Sample Input 1

3 2

Sample Output 1

10

The sum can take 10 values, as follows:

(10^{100})+(10^{100}+1)=2\times 10^{100}+1

(10^{100})+(10^{100}+2)=2\times 10^{100}+2

(10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2\times 10^{100}+3

(10^{100}+1)+(10^{100}+3)=2\times 10^{100}+4

(10^{100}+2)+(10^{100}+3)=2\times 10^{100}+5

(10^{100})+(10^{100}+1)+(10^{100}+2)=3\times 10^{100}+3

(10^{100})+(10^{100}+1)+(10^{100}+3)=3\times 10^{100}+4

(10^{100})+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+5

(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3\times 10^{100}+6

(10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4\times 10^{100}+6

Sample Input 2

200000 200001

Sample Output 2

1

We must choose all of the integers, so the sum can take just 1 value.

Sample Input 3

141421 35623

Sample Output 3

220280457

Solution in C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;

namespace AtCoder.D
{
    internal static class CR
    {
        public static string GetText() { return Console.ReadLine(); }
        public static List<string> GetTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long GetLong() { return long.Parse(Console.ReadLine()); }
        public static List<long> GetLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }
    }

    public class Program
    {
        public static long N { get; private set; }
        public static long K { get; private set; }

        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var inputs = CR.GetLongs();
            N = inputs[0];
            K = inputs[1];

            var mod = new Modular();
            for (long k = K; k <= N + 1; k++)
            {
                var min = k * (k + 1) / 2 - k;
                var max = (N - 1) * k + 2 * k - k * (k + 1) / 2;
                var count = max - min + 1;
                mod += count;
            }

            return mod;
        }
    }
    public class Modular
    {
        public long Value { get; private set; }

        private static readonly long _mod = (long)Math.Pow(10, 9) + 7;
        private static readonly List<int> _facCache = new List<int> { 1 };

        public static explicit operator long(Modular m) => m.Value;
        public static implicit operator Modular(long a)
        {
            var m = a % _mod;

            return new Modular
            {
                Value = (m < 0) ? m + _mod : m
            };
        }

        public static Modular operator +(Modular a, Modular b) => a.Value + b.Value;
        public static Modular operator -(Modular a, Modular b) => a.Value - b.Value;
        public static Modular operator *(Modular a, Modular b) => a.Value * b.Value;
        public static Modular operator /(Modular a, Modular b) => a * Pow(b, _mod - 2);
        public static Modular Pow(Modular a, long 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 Factorial(long n)
        {
            for (int i = _facCache.Count; i <= n; ++i)
            {
                var fac = (int)(Math.BigMul(_facCache.Last(), i) % _mod);
                _facCache.Add(fac);
            }
            return _facCache[(int)n];
        }
        public static Modular Combination(long n, long r)
        {
            Modular ans = 1;
            for (var i = 0; i < r; i++)
            {
                ans *= n - i;
            }
            for (var i = 1; i <= r; i++)
            {
                ans /= i;
            }

            return ans;
        }
        public override string ToString()
        {
            return Value.ToString();
        }
    }
}