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.Globalization;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Text;

namespace AtCoder
{
    static class Program_D
    {
        class Solver
        {
            int ri => sc.Integer();
            long rl => sc.Long();
            double rd => sc.Double();
            string rs => sc.Scan();
            public StreamScanner sc = new StreamScanner(Console.OpenStandardInput());



            // ABC163 Sum of Large Numbers
            public void Solve()
            {
                // 0,1,...,nのn+1個の数.
                //SumModTest();

                var n = ri;
                var kMin = ri;

                // k=1,kMin+1,...,n+1としたときのmod数を事前計算
                var minMods = new ModInt[n+1+1]; // 1offset
                var maxMods = new ModInt[n+1+1];
                minMods[1] = 0;
                maxMods[1] = n;

                for (int selNum = 2; selNum<=n+1; ++selNum)
                {
                    // selNum=2の時->+0,+1なので1になる様に.
                    minMods[selNum] = minMods[selNum - 1] + (ModInt)(selNum-1);
                    // selNum=2の時->+n,+(n-1)になるように
                    maxMods[selNum] = maxMods[selNum-1] + (ModInt) (n - selNum+1);
                }

                var sum = new ModInt();
                for (int k = kMin; k <= n + 1; ++k)
                {
                    // (n,kMin)=(3,2)の時,k=2,3,4が出るように
                    //Wl($"{k} {minMods[k]} {maxMods[k]}");
                    sum += maxMods[k] - minMods[k] + (ModInt)1;
                }

                Wl(sum);
                //Wl($"{minMod} {maxMod}");
            }

            private void SumModTest()
            {
                var tests = new[] {new[] {3, 4}, new[] {3, 3}, new[] {3, 2}, new[] {3, 1}};
                foreach (var test in tests)
                {
                    var n = test[0];
                    var k = test[1];
                    ModInt minMod = SumMod(0, k);
                    ModInt maxMod = SumMod(n - k + 1, k);
                    Wl($"({n} {k}) : ({minMod} {maxMod})");
                }
            }

            private ModInt SumMod(int start, int num)
            {
                var result = new ModInt(0);
                for (int i = 0; i < num; ++i)
                {
                    result+= new ModInt(start+i);
                }
                return result;
            }


            // ----------------------------------------------------------------------------
            static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }


            string Rl()
            {
                return Console.ReadLine();
            }
            void Wl(UInt64 val)
            {
                Console.WriteLine(val);
            }
            void Wl(Int64 val)
            {
                Console.WriteLine(val);
            }
            void Wl(uint val)
            {
                Console.WriteLine(val);
            }
            void Wl(int val)
            {
                Console.WriteLine(val);
            }
            void Wl(double val)
            {
                Console.WriteLine(val);
            }
            void Wl(string mes)
            {
                Console.WriteLine(mes);
            }
            public int Int()
            {
                return int.Parse(Console.ReadLine());
            }

            public int[] Ints(int subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => int.Parse(s) - subtract).ToArray();
            }
            public Int64[] Int64s(Int64 subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => Int64.Parse(s) - subtract).ToArray();
            }
            public UInt64[] UInt64s(UInt64 subtract)
            {
                return Console.ReadLine().Split(' ').Select(s => UInt64.Parse(s) - subtract).ToArray();
            }


        }



        static void Main(string[] args)
        {
            Console.SetOut(new Printer(Console.OpenStandardOutput()) { AutoFlush = false });
            new Solver().Solve();
            Console.Out.Flush();
        }
    }

    public class Printer : StreamWriter
    {
        public override IFormatProvider FormatProvider => CultureInfo.InvariantCulture;
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;

        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char()
        {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }

    struct ModInt
    {
        const int MOD = 1000000007;
        long Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public ModInt(long data) { if ((Data = data % MOD) < 0) Data += MOD; }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator long(ModInt modInt) => modInt.Data;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static implicit operator ModInt(long val) => new ModInt(val);
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, ModInt b)
        {
            long res = a.Data + b.Data;
            return new ModInt() { Data = res >= MOD ? res - MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator +(ModInt a, long b) => a.Data + b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, ModInt b)
        {
            long res = a.Data - b.Data;
            return new ModInt() { Data = res < 0 ? res + MOD : res };
        }
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator -(ModInt a, long b) => a.Data - b;
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator *(ModInt a, ModInt b) => new ModInt() { Data = a.Data * b.Data % MOD };
        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public static ModInt operator /(ModInt a, ModInt b) => a.Data * GetInverse(b);

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public override string ToString() => Data.ToString();

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        static long GetInverse(long a)
        {
            long div;
            long p = MOD;
            long x1 = 1, y1 = 0, x2 = 0, y2 = 1;
            while (true)
            {
                if (p == 1) return x2;
                div = a / p;
                x1 -= x2 * div;
                y1 -= y2 * div;
                a %= p;
                if (a == 1) return x1;
                div = p / a;
                x2 -= x1 * div;
                y2 -= y1 * div;
                p %= a;
            }
        }
    }

}