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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.DataInputStream;
import java.io.IOException;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author iavanish
 */
public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DSumOfLargeNumbers solver = new DSumOfLargeNumbers();
        solver.solve(1, in, out);
        out.close();
    }

    static class DSumOfLargeNumbers {

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            long mod = 1000000007;
            long n = in.nextLong();
            long k = in.nextLong();

            long sum = 0;
            for (long i = k; i <= n; i++) {
                long start = sum(i - 1);
                long end = sum(n) - sum(n - i);
                sum += (end - start + 1);
                sum %= mod;
            }

            out.println(sum + 1);
        }

        private long sum(long n) {
            return (n * (n + 1)) / 2;
        }

    }

    static class FastReader {

        private final int BUFFER_SIZE = 1 << 16;
        private final InputStream inputStream;
        private final byte[] buffer;
        private int bufferPointer;
        private int bytesRead;

        public FastReader() {
            this.inputStream = new DataInputStream(System.in);
            this.buffer = new byte[BUFFER_SIZE];
            this.bufferPointer = bytesRead = 0;
        }

        public FastReader(InputStream inputStream) {
            this.inputStream = inputStream;
            this.buffer = new byte[BUFFER_SIZE];
            this.bufferPointer = bytesRead = 0;
        }

        public FastReader(String fileName) {
            try {
                this.inputStream = new DataInputStream(new FileInputStream(fileName));
                this.buffer = new byte[BUFFER_SIZE];
                this.bufferPointer = bytesRead = 0;
            } catch (FileNotFoundException e) {
                throw new RuntimeException(e);
            }
        }

        public long nextLong() {
            long nextLong = 0;
            byte c = read();
            while (c <= ' ') {
                c = read();
            }
            boolean negative = (c == '-');
            if (negative) {
                c = read();
            }
            do {
                nextLong = nextLong * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (negative) {
                return -nextLong;
            }
            return nextLong;
        }

        private void fillBuffer() {
            try {
                bytesRead = inputStream.read(buffer, bufferPointer = 0, BUFFER_SIZE);
                if (bytesRead == -1) {
                    buffer[0] = -1;
                }
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        private byte read() {
            if (bufferPointer == bytesRead) {
                fillBuffer();
            }
            return buffer[bufferPointer++];
        }

    }

}