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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"math"
	"os"
	"strconv"
)

const INFINITY = math.MaxInt64/2 - 1

func exec(stdin *Stdin, stdout *Stdout) {
	n := stdin.ReadInt()
	k := stdin.ReadInt()

	min := 0
	max := 0
	for i := 0; i < k; i++ {
		min += i
		max += n - i
	}

	left := k
	right := n - k

	ans := 0
	for i := k; i <= n+1; i++ {
		ans += max - min + 1
		ans %= 1000000000 + 7
		min += left
		max += right
		left += 1
		right -= 1
	}

	stdout.Println(ans)
}

func main() {
	stdout := NewStdout()
	defer stdout.Flush()
	exec(NewStdin(bufio.ScanWords), stdout)
}

type Stdin struct {
	stdin *bufio.Scanner
}

func NewStdin(split bufio.SplitFunc) *Stdin {
	s := Stdin{bufio.NewScanner(os.Stdin)}
	s.stdin.Split(split)
	s.stdin.Buffer(make([]byte, bufio.MaxScanTokenSize), INFINITY)
	return &s
}

func (s *Stdin) Read() string {
	s.stdin.Scan()
	return s.stdin.Text()
}

func (s *Stdin) ReadInt() int {
	n, _ := strconv.Atoi(s.Read())
	return n
}

func (s *Stdin) ReadFloat64() float64 {
	n, _ := strconv.ParseFloat(s.Read(), 64)
	return n
}

func (s *Stdin) ReadIntSlice(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = s.ReadInt()
	}
	return a
}

func (s *Stdin) ReadStringSlice(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = s.Read()
	}
	return a
}

func (s *Stdin) ReadFloat64Slice(n int) []float64 {
	a := make([]float64, n)
	for i := 0; i < n; i++ {
		a[i] = s.ReadFloat64()
	}
	return a
}

type Stdout struct {
	stdout *bufio.Writer
}

func NewStdout() *Stdout {
	return &Stdout{bufio.NewWriter(os.Stdout)}
}

func (s *Stdout) Flush() {
	s.stdout.Flush()
}

func (s *Stdout) Println(a ...interface{}) {
	fmt.Fprintln(s.stdout, a...)
}

func Min(a int, b ...int) int {
	for _, v := range b {
		if v < a {
			a = v
		}
	}
	return a
}

func Max(a int, b ...int) int {
	for _, v := range b {
		if a < v {
			a = v
		}
	}
	return a
}

func Abs(x int) int {
	if x > 0 {
		return x
	} else {
		return x * -1
	}
}

func Pow(x, y int) int {
	z := 1
	for y > 0 {
		if y%2 == 0 {
			x *= x
			y /= 2
		} else {
			z *= x
			y -= 1
		}
	}
	return z
}

func CreateMatrix(x, y int) [][]int {
	matrix := make([][]int, x)
	for i := 0; i < x; i++ {
		matrix[i] = make([]int, y)
	}
	return matrix
}