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 rep(i,n); for(int i = 0;i < (int)(n);i++)
#define all(x) (x).begin(),(x).end()
typedef long long ll;
ll per(ll n,ll x){
    ll ans = 1;
    rep(i,x)ans *= n-i;
    rep(i,x)ans /= i+1;
    ans %= 1000000000+7;
    return ans;
}
int main(){
    int n,k;
    cin >> n >> k;
    ll ans = 0;
    vector<ll>sum(n+1);
    sum[0] = 0;
    rep(i,n)sum[i+1] = sum[i] + i+1;
    for(int i = k;i <= n+1;i++){
        ll big = 0,sma = 0;
        if(n-i < 0)big = sum[n];
        else big = sum[n] - sum[n-i];

        sma = sum[i-1];
        //cout << i << ' ' << big << ' ' << sma << endl;
        ans += big - sma+1;
        ans %= 1000000000+7;
    }
    cout << ans << endl;
    return 0;
}