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>
using namespace std;
#define ll long long 
#define endl "\n"
#define pb push_back
#define f(i,n) for(i=0;i<n;i++)
#define F(i,a,b) for(i=a;a<=b;i++)
#define arr(a,n) for( i=0;i<n;i++)cin>>a[i];
#define fi first
#define se second
#define mp make_pair
#define mod 1000000007
#define YES cout<<"YES"<<endl;
#define Yes cout<<"Yes"<<endl;
#define NO cout<<"NO"<<endl;
#define No cout<<"No"<<endl;
#define yes cout<<"yes"<<endl;
#define no cout<<"no"<<endl;
#define vi vector<ll>
#define ed end()
#define bg begin()
#define sz size()
#define ln length()
#define s() sort(a,a+n);
#define sr() sort(a,a+n,greater<ll>());
#define v()  sort(v.begin(),v.end());
#define vr() sort(v.begin(),v.end(),greater<ll>());
#define mod 1000000007
#define fast() ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
ll gcd(ll a, ll b){if(!b)return a;return gcd(b, a % b);}
ll power(ll x,ll y,ll p){ll res=1;x%=p;while(y>0){if(y&1)res=(res*x)%p;y=y>>1;x=(x*x)%p;}return res;}
int main() {
    /*#ifndef ONLINE_JUDGE
        // for getting input from input.txt
        freopen("input.txt", "r", stdin);
        // for writing output to output.txt
        freopen("output.txt", "w", stdout);
    #endif*/
        /* 
        Ofcourse it's Hard.
        It's supposed to be Hard.
        If it's easy everyone would do it.
        HARD IS WHAT MAKES IT GREAT

        YESTERDAY U SAID TOMORROW

        SLOWLY BECOMING THE PERSON I 
        SHOULD HAVE BEEN A LONG TIME AGO

        SAME TASK CAN'T BE FOUND DIFFICULT TWICE

        BTBHWSITW

        SPRH TU KAB P

        CP IS ALL ABOUT THINKING 
        YOU HAVE MUCH MORE POTENTIAL THAN U THINK

        AJIT SHIDDAT 10

        UR DAILY ROUTINE 


        */

fast();
//ll t;cin>>t;while(t--)
{
    ll n,k;
    cin>>n>>k;
    ll ans=0;
    for(int i=k;i<=n;i++)
    {   
        ll mn=(ll)(i*(ll)(i-1))/2;

        double mx=((double(i/double(2.0)))*((2*(n-i+1)+(i-1))));
         ll mxx=mx;
        //cerr<<mxx<<" "<<mn<<endl;
        ans=((ans+(mxx%mod-mn%mod+mod)) + 1);
        //cout<<ans<<endl;
    }
    cout<<(ans+1)%mod<<endl;
    
}
return 0;
}