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)

macro_rules! read {
	() => {{
		let mut buf = String::new();
		std::io::stdin().read_line(&mut buf).unwrap();
		buf
	}};
	( Vec<$t:ty> ) => {
		read!()
			.trim()
			.split_whitespace()
			.map(|x| x.parse::<$t>().unwrap())
			.collect::<Vec<_>>()
	};
	( $( $t:ty ),* ) => {{
		let buf = read!();
		let mut iter = buf.split_whitespace().collect::<Vec<_>>().into_iter();
		( $( iter.next().unwrap().parse::<$t>().unwrap() ),* )
	}};
}

const MOD: i64 = 1000000007;

fn main() {
	let (n, k) = read!(i64, i64);

	let mut min = k * (k - 1) / 2;
	let mut max = k * (n + (n - k + 1)) / 2;
	let mut ans = 0;

	for i in k..(n + 2) {
		ans += max - min + 1;
		ans %= MOD;

		min += i;
		max += n - i;
	}

	println!("{}", ans)
}