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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

const MOD: i64 = 1000000007;

fn main() {
    input! {
        n: i64,
        k: i64,
    }

    let mut small_sum: i64 = 0;
    let mut large_sum: i64 = 0;

    for i in 0..k {
        small_sum += i;
        small_sum %= MOD;
        if small_sum < 0 {
            small_sum += MOD;
        }

        large_sum += n - i;
        large_sum %= MOD;
        if large_sum < 0 {
            large_sum += MOD;
        }
    }

    let mut ans: i64 = 0;
    for take in k..=(n + 1) {
        // dbg!(take, large_sum);
        ans += large_sum - small_sum + 1;
        ans %= MOD;
        if ans < 0 {
            ans += MOD;
        }

        small_sum += take;
        small_sum %= MOD;
        if small_sum < 0 {
            small_sum += MOD;
        }

        large_sum += n - take;
        large_sum %= MOD;
        if large_sum < 0 {
            large_sum += MOD;
        }

    }

    println!("{}", ans);
}