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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::collections::HashMap;

fn main() {
  input! {
    N: i128,
    K: i128,
  }
  
  let quotient = N / K;
  let mut n = if 0 < quotient {
    N - (K * quotient)
  } else {
    N
  };
    
  let mut map: HashMap<i128, bool> = HashMap::new();
  let mut result = i128::max_value();
  while map.get(&n).is_none() {
    map.insert(n, true);
    result = std::cmp::min(n, result);
    n = (n - K).abs();
  }
  println!("{}", result);
}