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 int long long
#define tc int t; cin>>t; while(t--)
#define speed ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define mod 1000000007
#define pb push_back
#define vi vector<int>
#define vc vector<char>
#define eb emplace_back
#define pii pair<int,int>
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define fo(i,x,n) for(int i=x;i<n;i++)
#define csb(x) __builtin_popcount(x)
#define tz(x) __builtin_ctz(x)
#define lsbp(x) __builtin_ffs(x)
#define msbp(x) __lg(x)
#define btoi(str,i) stoi(str,0,i)
#define ff first
#define ss second
const int inf=0x3f3f3f3f3f3f3f3f;

void zz(){
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
}

int32_t main(){
zz();
int n,k;cin>>n>>k;
int z=0;
int x=0;
for(int i=k;i<=n+1;i++){
   x=(i*(i-1))/2;
   x-=1;
   int y=(i*(2*(n-i+1)+(i-1)))/2;
   z+=(y-x);
   //z+=y;
   //cout<<y<<" "<<x<<endl;
   z%=mod;
}
cout<<z<<endl;

}