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 std::io::{stdin, stdout, StdinLock, StdoutLock, BufReader, BufWriter, BufRead, Write};

fn main() {
    let (std_in, std_out) = (stdin(), stdout());
    let mut io = IO::new(std_in.lock(), std_out.lock());
    let tmp = io.rv::<i64>();
    let (n, k) = (tmp[0], tmp[1]);
    let M = 1000000007;

    let mut ans = 0;
    for i in k..=n+1 {
        let le = i * (i - 1) / 2;
        let ri = i * (2 * n + 1 - i) / 2;
        let dist = ri - le + 1;
        ans = (ans + dist) % M;
    }
    io.w(std::cmp::min(ans, M));
}


struct IO<'a> {
    br: BufReader<StdinLock<'a>>,
    bw: BufWriter<StdoutLock<'a>>,
}

#[allow(dead_code)]
impl IO<'_> {
    fn new<'a>(il: StdinLock<'a>, ol: StdoutLock<'a>) -> IO<'a> {
        IO {br: BufReader::new(il), bw: BufWriter::new(ol) }
    }

    fn r<T: std::str::FromStr>(&mut self) -> T {
        let mut buf = String::new();
        self.br.read_line(&mut buf).ok();
        buf.trim().parse().ok().unwrap()
    }

    fn rb(&mut self) -> Vec<u8> {
        let mut buf = String::new();
        self.br.read_line(&mut buf).ok();
        buf.trim().as_bytes().to_vec()
    }

    fn rv<T: std::str::FromStr>(&mut self) -> Vec<T> {
        let mut buf = String::new();
        self.br.read_line(&mut buf).ok();
        buf.trim().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
    }

    fn rvb(&mut self) -> Vec<Vec<u8>> {
        let mut buf = String::new();
        self.br.read_line(&mut buf).ok();
        buf.trim().split_whitespace().map(|e| e.as_bytes().to_vec()).collect()
    }

    fn w<T: std::fmt::Display>(&mut self, x: T) {
        let _ = writeln!(self.bw, "{}", x);
    }

    fn wb(&mut self, s: &[u8]) {
        let _ = writeln!(self.bw, "{}", unsafe{std::str::from_utf8_unchecked(s)});
    }

    fn wv<T: std::fmt::Display>(&mut self, v: &[T]) {
        let _ = write!(self.bw, "{}", v[0].to_string());
        for x in v[1..].iter() {
            let _ = write!(self.bw, " {}", x.to_string());
        }
        let _ = writeln!(self.bw);
    }

    fn wvb(&mut self, v: &[Vec<u8>]) {
        let _ = write!(self.bw, "{}", unsafe{std::str::from_utf8_unchecked(&v[0])});
        for x in v[1..].iter() {
            let _ = write!(self.bw, " {}", unsafe{std::str::from_utf8_unchecked(x)});
        }
        let _ = writeln!(self.bw);
    }
}