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++ (GCC 9.2.1) (judge verdict: Accepted)

#include<cstdio>
#include<cstring>
#include<string>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<queue>
#include<map>
#include<ctime>

using namespace std;

template <typename T>

inline T read()
{
	T x=0,f=1;char c=getchar();
	while(!isdigit(c))
	{if(c=='-') f=-f;c=getchar();}
	while(isdigit(c))
	{x=(x<<3)+(x<<1)+(c-48);c=getchar();}
	return x*f;
}

#define lint long long int
#define ulint unsigned lint

const int inf=1e9+1e7;
const int Mod=1e9+7;

lint ans=0;
lint n,k;

int main(void)
{

	//freopen("testdata.in","r",stdin);
	//freopen("testdata.out","w",stdout);

	scanf("%lld%lld",&n,&k);

	for(lint i=k;i<=n+1;i++)
	{
		ans+=(n+n-i+1)*i/2-(i-1)*i/2+1;
		ans%=Mod;
		// printf("%lld\n",ans);
	}

	printf("%lld\n",ans);

	return 0;

}