Problem:
Score : 300 points

Problem Statement

Given any integer x, Aoki can do the operation below.

Operation: Replace x with the absolute difference of x and K.

You are given the initial value of an integer N. Find the minimum possible value taken by N after Aoki does the operation zero or more times.

Constraints

0 ≤ N ≤ 10^{18}

1 ≤ K ≤ 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the minimum possible value taken by N after Aoki does the operation zero or more times.

Sample Input 1

7 4

Sample Output 1

1

Initially, N=7.

After one operation, N becomes |7-4| = 3.

After two operations, N becomes |3-4| = 1, which is the minimum value taken by N.

Sample Input 2

2 6

Sample Output 2

2

N=2 after zero operations is the minimum.

Sample Input 3

1000000000000000000 1

Sample Output 3

0

Solution in Rust (1.15.1) (judge verdict: Time Limit Exceeded)

use std::cmp::*;
use std::collections::BTreeSet;
use std::io::*;
use std::str::FromStr;
//portable utility
#[allow(dead_code)]
fn switch<T>(flag: bool, true_value: T, false_value: T) -> T {
    if flag {
        true_value
    } else {
        false_value
    }
}

#[allow(dead_code)]
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn read_string() -> Vec<char> {
    read::<String>().chars().collect()
}

#[allow(dead_code)]
fn read_vector<T: FromStr>(number: i32) -> Vec<T> {
    (0..number).map(|_| read()).collect()
}

fn main() {
    let mut n: i64 = read();
    let k: i64 = read();
    let mut history = BTreeSet::new();
    let mut min = n;
    loop {
        let next = (n - k).abs();
        if history.get(&next).is_some() {
            println!("{}", min);
            return;
        }
        n = next;
        if next < min {
            min = next;
        }
        history.insert(next);
    }
}