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 <algorithm>
#include <stdio.h>
#include <iostream>
#include <cstdlib>
#include <vector>
#include <queue>
#include <math.h>
#include <string> 
#include <bits/stdc++.h>
using namespace std;

int main(){
    long long MOD;
    MOD = 1000000007;
    int n,k;
    cin >> n >> k;
    vector<long long> min(n+1);
    vector<long long> max(n+1);
    min[0]=0;
    max[0]=0;
    for(int i=1;i<n+2;i++){
        min[i] = min[i-1]+i-1;
        max[i] = max[i-1]+(n+1-i);
    }
    int ans;
    ans=0;
    for(int i=k;i<n+2;i++){
        ans = ans + (max[i]-min[i]+1)%MOD;
        ans = ans%MOD;
    }
    cout << ans;
    return 0;
}