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)

//#define _GLIBCXX_DEBUG
#include<bits/stdc++.h>
#define PI 3.14159265359
using namespace std;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
const long long INF= 1e+18+1;
typedef long long ll;
typedef vector<ll> vl;
typedef vector<vector<ll> >vvl;
typedef pair<ll,ll> P;
typedef tuple<ll,ll,ll> T;
const ll MOD=1000000007LL;
string abc="abcdefghijklmnopqrstuvwxyz";
string ABC="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
int main(){
  ll n,k;cin>>n>>k;
  vl sum(n+1);
  vl resum(n+1);
  sum[0]=0;
  resum[n]=n;
  for(ll i=1;i<=n;i++){
    sum[i]=sum[i-1]+i;
  }
  for(ll i=n-1;i>=0;i--){
    resum[i]=resum[i+1]+i;
  }
  ll ans=0;
  for(ll i=k-1;i<=n;i++){
    ans+=resum[n-i]-sum[i]+1;
    //cout<<resum[n-i]<<" "<<sum[i]<<endl;
    ans%=MOD;
  }
  cout<<ans<<endl;
}