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(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let k: usize = sc.cin();

    let mut ans = ModInt(0, M);

    let mut w = ModInt(n as i64 + 1, M);
    for c in 1..=n+1 {  // c 子使う
        if c > 1 {
            w += ModInt(n as i64 + 2 - 2 * c as i64, M);
        }
        // trace!(c, w);
        if c >= k {
            // trace!(ans, w);
            ans = ans + w;
            // trace!(ans);
            // if ans.0 < 0 { break }
        }
    }
    put!(ans);
}

#[derive(Debug, PartialEq, Eq, Clone, Copy)]
struct ModInt(i64, i64);  // (residual, modulo)
impl ModInt {
    fn unwrap(self) -> i64 { self.0 }
    fn inv(self) -> Self {
        fn exgcd(r0: i64, a0: i64, b0: i64, r: i64, a: i64, b: i64)
                -> (i64, i64, i64) {
            if r > 0 {
                exgcd(r, a, b, r0 % r, a0 - r0 / r * a, b0 - r0 / r * b)
            } else {
                (a0, b0, r0)
            }
        }
        let (a, _, r) = exgcd(self.0, 1, 0, self.1, 0, 1);
        if r != 1 { panic!("{:?} has no inverse!", self); }
        ModInt(((a % self.1) + self.1) % self.1, self.1)
    }
    fn pow(self, n: i64) -> Self {
        if n < 0 {
            self.pow(-n).inv()
        } else if n == 0 {
            ModInt(1, self.1)
        } else if n == 1 {
            self
        } else {
            let mut x = (self * self).pow(n / 2);
            if n % 2 == 1 { x *= self }
            x
        }
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
impl std::ops::Neg for ModInt {
    type Output = Self;
    fn neg(self) -> Self {
        if self.0 == 0 { return self }
        ModInt(self.1 - self.0, self.1)
    }
}
impl std::ops::Add<i64> for ModInt {
    type Output = Self;
    fn add(self, other: i64) -> Self {
        let mut res = self.0 + other;
        while res >= self.1 { res -= self.1 }
        while res < 0 { res += self.1 }
        ModInt(res, self.1)
    }
}
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, other: ModInt) -> Self { self + other.0 }
}
impl std::ops::Add<ModInt> for i64 {
    type Output = ModInt;
    fn add(self, other: ModInt) -> ModInt { other + self }
}
impl std::ops::AddAssign<i64> for ModInt {
    fn add_assign(&mut self, other: i64) {
        self.0 += other;
        if self.0 >= self.1 { self.0 -= self.1; }
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, other: ModInt) { *self += other.0; }
}
impl std::ops::Sub<i64> for ModInt {
    type Output = Self;
    fn sub(self, other: i64) -> Self {
        let res = if self.0 < other {
            self.0 + self.1 - other
        } else {
            self.0 - other
        };
        ModInt(res, self.1)
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, other: ModInt) -> Self { self - other.0 }
}
impl std::ops::Sub<ModInt> for i64 {
    type Output = ModInt;
    fn sub(self, other: ModInt) -> ModInt { -other + self }
}
impl std::ops::SubAssign<i64> for ModInt {
    fn sub_assign(&mut self, other: i64) {
        if self.0 < other {
            self.0 = self.1 - other + self.0;
        } else {
            self.0 -= other;
        }
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, other: ModInt) { *self -= other.0; }
}
impl std::ops::Mul<i64> for ModInt {
    type Output = Self;
    fn mul(self, other: i64) -> Self { ModInt((self.0 * other) % self.1, self.1) }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, other: ModInt) -> Self { self * other.0 }
}
impl std::ops::Mul<ModInt> for i64 {
    type Output = ModInt;
    fn mul(self, other: ModInt) -> ModInt { other * self }
}
impl std::ops::MulAssign<i64> for ModInt {
    fn mul_assign(&mut self, other: i64) { self.0 = (self.0 * other) % self.1; }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, other: ModInt) { *self *= other.0; }
}
impl std::ops::Div<i64> for ModInt {
    type Output = Self;
    fn div(self, other: i64) -> Self { self * ModInt(other, self.1).inv() }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, other: ModInt) -> Self { self * other.inv() }
}
impl std::ops::Div<ModInt> for i64 {
    type Output = ModInt;
    fn div(self, other: ModInt) -> ModInt { other.inv() * self }
}
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, other: ModInt) { self.0 = (self.0 * other.inv().0) % self.1; }
}
impl std::ops::DivAssign<i64> for ModInt {
    fn div_assign(&mut self, other: i64) { *self /= ModInt(other, self.1); }
}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}