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: Wrong Answer)

use std::io::*;
use std::str::FromStr;
//portable utility
#[allow(dead_code)]
fn switch<T>(flag: bool, true_value: T, false_value: T) -> T {
    if flag {
        true_value
    } else {
        false_value
    }
}
#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}
#[allow(dead_code)]
fn read_string() -> Vec<char> {
    read::<String>().chars().collect()
}
#[allow(dead_code)]
fn read_vector<T: FromStr>(number: usize) -> Vec<T> {
    (0..number).map(|_| read()).collect()
}

fn frac(x: i128) -> i128 {
    let mut ans = 1;
    for xx in 2..=x {
        ans *= xx;
    }
    ans
}

fn p(n: i128, r: i128) -> i128 {
    let mut ans = 1;
    for xx in n - r + 1..=n {
        ans *= xx;
    }
    ans
}

fn comp(n: i128, r: i128) -> i128 {
    //p(n, r) / frac(r)
    let mut y = 1;
    let mut ans = 1;
    let l: i128 = num::pow::pow(10, 9) + 7;
    for xx in n - r + 1..=n {
        ans = (ans * xx) % l;
        while ans % y == 0 && y <= r {
            ans /= y;
            y += 1;
        }
    }
    ans
}

fn main() {
    let (n, k): (i128, i128) = (read(), read());

    println!("{}", comp(n + k, n + 1 - k));
}