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::*;

fn read_int(s: &mut StdinLock) -> usize {
    s.by_ref().bytes().map(|c| c.unwrap() as char)
        .take_while(|c| !c.is_whitespace())
        .skip_while(|c| c.is_whitespace())
        .fold(0, |a, x| (x as u8 - b'0') as usize + a * 10)
}
fn main(){
    let s = stdin();
    let mut s = s.lock();
    let n = read_int(&mut s);
    let k = read_int(&mut s);
    let mut old_mins: usize = 0;
    let mut old_maxs: usize = 0;
    let mut ans: usize = 0;
    for i in 0..n {
        old_mins = old_mins + i;
        old_maxs = old_maxs + n - i;
        if i >= k - 1 {
            ans = (ans + old_maxs - old_mins + 1)%1000000007;
        }
    }
    println!("{}", ans+1);
}