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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long N = in.nextLong();
        long K = in.nextLong();

        if (K == 1) {
            System.out.println(K);
            return;
        }

        long slow = N;
        long fast = absoluteDiff(absoluteDiff(N, K), K);
        long min = slow;

        while (slow != fast) {
            min = Math.min(Math.min(min, slow), fast);
            slow = absoluteDiff(slow, K);
            fast = absoluteDiff(absoluteDiff(fast, K), K);
        }

        System.out.println(min);

    }

    public static long absoluteDiff(long a, long b) {
        return Math.abs(a - b);
    }

}