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<stdio.h>
//#include <bits/stdc++.h>
#include<vector>
#include<float.h>
#include<iomanip>
#include<algorithm>
#include<string>
#include<cstring>
#include<math.h>
#include<cmath>
#include<sstream>
#include<set>
#include<map>
#include<queue>
#include <cassert>
#include <cmath>
#include<cstdint>


#define rep(i,n)for(int i=0;(i)<(int)(n);i++)
#define REP(i,a,b)for(int i=(int)(a);(i)<=(int)(b);i++)
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define vec(type,n) vector<type>(n)
#define vvec(m,n) vector<vector<int>> (int(m),vector<int>(n))
#define ALL(a)  (a).begin(),(a).end()

using namespace std;
using ll = long long;
using Graph = vector<vector<int>>;
using P = pair<int,int>;

vector<int>bitSearch(int bit,int n){
    vector<int>S,False(1,-1);
    rep(i,n)if(bit&(1<<i))S.push_back(i);
    return S;
}

template<typename A,size_t N,typename T>
void Fill(A(&array)[N],const T &val){
    fill((T*)array,(T*)(array+N),val);
}


ll gcd(ll a,ll b){
    if(a%b==0)return b;
    else return gcd(b,a%b);
}

const int MOD = 1e9 + 7;
int main(){
    int n, k;
    cin >> n >> k;
    ll res = 0, sum = 1;

    ll l = 0, r = n;
    REP(i, 1, n + 1){
        if(i > 1)l++;
        if(i > 1)r--;
        sum += (r - l);
        if(i >= k)res += sum;
        res %= MOD;
        sum %= MOD;
      //cout << sum << " " << res << endl;
    }
  if(res < 0)res += MOD;
    cout << res << endl;
}