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)

pub struct Scanner {
    line: Vec<String>,
    idx: usize,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        return Scanner {
            line: vec![],
            idx: 0,
        };
    }
    fn next<T: std::str::FromStr>(&mut self) -> T {
        if self.idx == self.line.len() {
            let mut buffer = String::new();
            std::io::stdin().read_line(&mut buffer).ok();
            let a: Vec<&str> = buffer.trim().split(' ').collect();
            self.line = a.iter().map(|&s| String::from(s)).collect();
            self.idx = 0;
        }
        let ret: T = self.line[self.idx].parse::<T>().ok().expect("Parse error.");
        self.idx += 1;
        ret
    }
    fn next_string(&mut self) -> Vec<char> {
        let s: String = self.next();
        return s.chars().collect::<Vec<char>>();
    }
    fn next_vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        let mut v: Vec<T> = Vec::with_capacity(n);
        for _i in 0..n {
            v.push(self.next());
        }
        v
    }
}

const MOD : u64 = 1_000_000_007;

fn main(){
    let mut scan = Scanner::new();
    let n: u64 = scan.next();
    let k: u64 = scan.next();
    let mut ans:u64 = 0;

    for i in k..n+2{
        let c: u64 = i;
        let min = (c - 1) * c / 2;
        let max = (n + 1 - c + n) * c / 2;
        ans += max - min + 1;
        ans %= MOD;
    }
    println!("{}", ans);
}