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)

#[warn(dead_code)]
fn read<T: std::str::FromStr>() -> T {
   let mut s = String::new();
   std::io::stdin().read_line(&mut s).ok();
   s.trim().parse().ok().unwrap()
}

#[warn(dead_code)]
fn readn<T: std::str::FromStr>(delimiter: &str) -> Vec<T> {
   let s = read::<String>();
   s.split(delimiter)
      .map(|e| e.parse().ok().unwrap())
      .collect::<Vec<T>>()
}

fn calc(n:i64, k:i64) -> (i64) {
    k * (n+n-k+1) / 2 - k * (k-1) / 2 + 1
}

fn main() {
    let nk = readn::<i64>(" ");
    let n = nk[0];
    let k = nk[1];
    let m = 1000000007 as i64;
    let mut ans: i64 = 0;
    for i in k..(n+2) {
        ans += calc(n, i) % m;
        ans %= m;
    }
    println!("{}", ans);
}