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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val n = sc.nextLong()
    val k = sc.nextLong()
    println(problem161c(n, k))
}

fun problem161c(n: Long, k: Long): Long {
    if (n == k) return 0
    var x = n
    if (x > k) {
        if (x % k == 0L) return 0
        var tmp = x
        var count = 0
        while (tmp > k) {
            tmp /= k
            count++
//            debugLog("a", x)
        }
        x /= count
        var prev = Long.MAX_VALUE
        while (true) {
            prev = x
            x = Math.abs(x - k)
//            debugLog("b", x)
            if (prev <= x) break
        }
        return prev
    }

    var prev: Long
    while (true) {
        prev = x
        x = Math.abs(x - k)
        if (prev <= x) {
            break
        }
    }
    return prev
}