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<iostream>
#include<vector>
#include<algorithm>
#include<stdlib.h>
#include<utility>
#include<functional>
#include<cfenv>
#include<cmath>
#include<string>
#include<queue>
#include<stack>
#include<map>
#include<set>

#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define vint vector<int>
#define vvint vector<vint>
#define P pair<int,int>
#define INT_MAX 2147483647
#define MOD 1000000007
#define PI 3.14159265358979323846
using namespace std;
typedef long long ll;

#define MAX 1000000000000



int main(void) {
	ll n, k; cin >> n >> k;
	ll ans = 0;
	for (ll i = k; i <= n;i++) {
		ll min, max;
		min = ((i - 1)*i) / 2;
		max = (i*(2 * n - i + 1)) / 2;
		ans = (ans+ max - min + 1)%MOD;
	}
	cout << (ans+1) % MOD << endl;
	return 0;
}