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 <algorithm>
#include <cmath>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <numeric>
#include <set>
#include <stack>
#include <string>
#include <vector>

using namespace std;
using LLONG = long long;
const LLONG MOD = 1000000007;

int main()
{
    LLONG N, K; cin >> N >> K; // N <= 2 * 1e5
    // 全ての数を選んでも1e5程度なので，余りが一巡することはない
    // Kの値が異なるとき，1e100の項の数が異なるので，値は全て異なる
    // K個選択するとき，最小値は0+...+(K-1)=K(K-1)/2，
    // 最大値は(N-K+1)+...+N=K(2N-K+1)/2で，間の値は全て作れる
    LLONG ans = 0;
    for (LLONG k = K; k <= N + 1; ++k)
    {
        LLONG max = k * (2 * N - k + 1) / 2;
        LLONG min = k * (k - 1) / 2;
        LLONG tmp = max - min + 1;
        ans += tmp;
        ans %= MOD;
    }
    cout << ans << endl;
}