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;
using s64 = int64_t;
using u64 = uint64_t;

template <typename T> T mod_sub (T a, T b, T m);

int main() {
	u64 N, K;
	cin >> N >> K;
	
	u64 mod = pow(10, 9) + 7;
	
	vector<u64> biggers(N+1, N);
	vector<u64> smallers(N+1);
	
	for(u64 i=1; i<=N; i++) {
		smallers[i] = smallers[i-1] + i;
		biggers[i]  = biggers[i-1] + N - i;
	}
	
	u64 ans = 0;
	
	for(u64 i=K-1; i<=N; i++) {
		ans = (ans + mod_sub(biggers[i] + 1, smallers[i], mod)) % mod;
	}
	
	cout << ans;
	
	return 0;
}

template <typename T> T mod_sub (T a, T b, T m) {
	return (a < b) ? m + a - b : (a - b) % m;
}