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)

#![allow(dead_code, unused_mut, unused_variables, unused_imports)]

use std::collections::{HashMap, HashSet, VecDeque};
use std::io::*;
struct Io<'a> {
    r: BufReader<StdinLock<'a>>,
    w: BufWriter<StdoutLock<'a>>,
    buf: VecDeque<String>,
    buf_str: String,
}
impl<'a> Io<'a> {
    fn r<T: std::str::FromStr>(&mut self) -> T {
        if self.buf.len() == 0 {
            self.r.read_line(&mut self.buf_str).unwrap();
            for w in self.buf_str.split_whitespace() {
                self.buf.push_back(w.to_owned());
            }
            self.buf_str.clear();
        }
        self.buf
            .pop_front()
            .unwrap()
            .parse()
            .unwrap_or_else(|_| panic!())
    }
    fn w<T: std::fmt::Display>(&mut self, v: T) {
        writeln!(self.w, "{}", v).unwrap();
    }
    fn iter<'b, T: std::str::FromStr>(&'b mut self) -> IoIter<'a, 'b, T> {
        IoIter {
            io: self,
            p: std::marker::PhantomData,
        }
    }
}
struct IoIter<'a: 'b, 'b, T: std::str::FromStr> {
    io: &'b mut Io<'a>,
    p: std::marker::PhantomData<T>,
}
impl<'a, 'b, T: std::str::FromStr> Iterator for IoIter<'a, 'b, T> {
    type Item = T;
    fn next(&mut self) -> Option<T> {
        Some(self.io.r())
    }
}
fn main() {
    let stdin = stdin();
    let stdout = stdout();
    let r = BufReader::new(stdin.lock());
    let w = BufWriter::new(stdout.lock());
    let io = Io {
        r: r,
        w: w,
        buf: VecDeque::new(),
        buf_str: String::new(),
    };
    problem(io);
}

fn problem(mut io: Io) {
    let n: usize = io.r();
    let k: usize = io.r();

    let ret: usize = (k..=n + 1)
        .map(|i: usize| {
            let min: usize = (0..i).sum();
            let max: usize = (n + 1 - i..=n).sum();
            max - min + 1
        })
        .fold(0, |acc, i| {
            let mut sum = acc + i;
            while sum > 1000000007 {
                sum -= 1000000007;
            }
            sum
        });
    io.w(ret);
}