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

namespace Main
{
    class Program
    {
        static void Main(string[] args)
        {
            //ここから
            //string[] str = Console.ReadLine().Split(' ');
            //int n = int.Parse(Console.ReadLine());

            string[] str = Console.ReadLine().Split(' ');

            long n = int.Parse(str[0]);
            long k = int.Parse(str[1]);

            long min = k * (k - 1) / 2;
            long max = k * n - min;

            long ans = max - min + 1;
            ans %= 1000000007;

            //Console.WriteLine("ans is {0}", ans);

            for(long i=k+1; i < n + 2; i++)
            {
                min += i - 1;
                max += n - i + 1;

                if(min>1000000007 && max > 1000000007)
                {
                    long temp = min / 1000000007;
                    min -= 1000000007*temp;
                    max -= 1000000007*temp;
                }
                ans += max - min + 1;
                ans %= 1000000007;
                //Console.WriteLine("i={0} のとき、min={1}, max={2}, ans={3}", i, min, max, ans);
                /*if (ans < 0)
                {
                    Console.WriteLine("yabai");
                    return;
                }*/
            }


            Console.WriteLine(ans);
        }
    }

}