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"
	"os"
	"strconv"
)
const mod = 1000000007
func main() {
	scanInit()
	n := scanInt()
	K := scanInt()
	// 全部で 0 ~ NまでのN+1の数列
	mins := make([]int,n+1)
	maxs := make([]int,n+1)
	minsum := 0
	maxsum := 0
	for i:= 0; i<=n; i++ {
		minsum += i
		maxsum += n-i
		maxs[i] += maxsum
		mins[i] += minsum
	}
	sum := 0
	for i:= K-1; i<n; i++ {
		// fmt.Println(i,maxs[i]-mins[i]+1)
		// この中から
		//K
		// 個以上の数を選ぶとき、その和としてあり得るものの個数
		//この日本語解釈むずすぎだろ
		sum += (maxs[i]-mins[i]+1) % mod
	}
	sum += 1
	sum %= mod
	fmt.Println(sum)
}

var sc = bufio.NewScanner(os.Stdin)
func scanInit () {
	sc.Split(bufio.ScanWords)
}
func scanInt () int{
sc.Scan()
	i,_ := strconv.Atoi(sc.Text())
	return i
}
//func scan () string{
//  sc.Scan()
//	return sc.Text()
//}