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;
typedef long long ll;
typedef long double ld;
constexpr ll INF = LLONG_MAX;
constexpr double DINF = DBL_MAX;
constexpr ll mod = 1e9+7;
constexpr double PI = M_PI;

template<typename T>
vector<T> make_v(size_t a){
  return vector<T>(a);
}
 
template<typename T, typename... Ts>
auto make_v(size_t a, Ts... ts){
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

int main(){
  cin.tie(0);
  cout.tie(0);
  ios::sync_with_stdio(false);
 
  long long n, k, ans = 0;
  cin >> n >> k;
  long long ma, mi;
  for(ll i = k; i <= n+1; i++){
    ma = i*(2*n+1-i)/2;
    mi = i*(i-1)/2;
    ans += ma-mi+1;
    ans %= mod;
  }
  cout << ans << endl;
  return 0;
}