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<bits/stdc++.h>
//cervello|Phoenix
using namespace std;
#define ll long long int
#define eb emplace_back
#define mk make_pair
#define pr pair<int,int>
#define all(x) x.begin(),x.end()
#define mod 1000000007

int main(){
  ios_base::sync_with_stdio(false);
    // #ifndef ONLINE_JUDGE
    //   freopen("input.txt", "r", stdin);
    //   freopen("output.txt", "w", stdout);
    // #endif
    ll n,k; cin>>n>>k;
    // ll ans=ncrfermet(n+k,k);
    // // ans*=(n-k);
    // ans%=mod;
    ll ans=0;
    if(n==1&&k==1)
      ans=3;
    // else if(n==1&&k>n+1)
    //   ans=0;
    else if(n==1)
      ans=1;
    else{
      for(ll i=k;i<=n+1;i++){
        ans+=(i*(n-i+1)+1)%mod;
        ans%=mod;
      }
    }
    cout<<ans<<"\n";
  return 0;
}