Problem:
Score : 300 points

Problem Statement

Takahashi, who lives on the number line, is now at coordinate X. He will make exactly K moves of distance D in the positive or negative direction.

More specifically, in one move, he can go from coordinate x to x + D or x - D.

He wants to make K moves so that the absolute value of the coordinate of the destination will be the smallest possible.

Find the minimum possible absolute value of the coordinate of the destination.

Constraints

-10^{15} \leq X \leq 10^{15}

1 \leq K \leq 10^{15}

1 \leq D \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

X K D

Output

Print the minimum possible absolute value of the coordinate of the destination.

Sample Input 1

6 2 4

Sample Output 1

2

Takahashi is now at coordinate 6. It is optimal to make the following moves:

Move from coordinate 6 to (6 - 4 =) 2.

Move from coordinate 2 to (2 - 4 =) -2.

Here, the absolute value of the coordinate of the destination is 2, and we cannot make it smaller.

Sample Input 2

7 4 3

Sample Output 2

1

Takahashi is now at coordinate 7. It is optimal to make, for example, the following moves:

Move from coordinate 7 to 4.

Move from coordinate 4 to 7.

Move from coordinate 7 to 4.

Move from coordinate 4 to 1.

Here, the absolute value of the coordinate of the destination is 1, and we cannot make it smaller.

Sample Input 3

10 1 2

Sample Output 3

8

Sample Input 4

1000000000000000 1000000000000000 1000000000000000

Sample Output 4

1000000000000000

The answer can be enormous.

Solution in Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;


public class Main {

    static void solve() {
        Scanner scan = new Scanner(System.in);

        long x = scan.nextLong();
        long k = scan.nextLong();
        long d = scan.nextLong();

        if(Math.abs(d) == Math.abs(x)) {
            if(d%2 == 0) {
                System.out.println(Math.abs(x));
                return;
            }
            System.out.println(0);
            return;
        }

        if(Math.abs(d) > Math.abs(x)) {
            long res1 = x + d;
            long res2 = x - d;
            long res = Math.min(Math.abs(res1), Math.abs(res2));
            System.out.println(res);
            return;
        }
        long st = Math.abs(x)%Math.abs(d);
        if(st > k) {
            st = k;
        }
        List<Long> list = new ArrayList<>();
        long add = st * Math.abs(d);
        long res1 = x + add;
        long res2 = x - add;
        list.add(Math.abs(res1));
        list.add(Math.abs(res2));
        if(st<k) {
            long res3 = res1 + d;
            long res4 = res1 - d;
            long res5 = res2 + d;
            long res6 = res2 - d;
            list.add(Math.abs(res3));
            list.add(Math.abs(res4));
            list.add(Math.abs(res5));
            list.add(Math.abs(res6));
        }
        Collections.sort(list);
        System.out.println(list.get(0));
        return;

//        st = k;
//        long add = st * Math.abs(d);
//        long res1 = x + add;
//        long res2 = x - add;
//        long res = Math.min(Math.abs(res1), Math.abs(res2));
//        System.out.println(res);

//        int t = scan.nextInt();
//        for (int i = 0; i < t; i++) {
//            int n = scan.nextInt();
//            int[] arr1 = new int[n];
//            for (int j = 0; j < n; j++) {
//                arr1[j] = scan.nextInt();
//            }
////            scase(n, arr1);
//        }


//        long t = scan.nextLong();

//        for (int i = 0; i < t; i++) {
//            int n = scan.nextInt();
////            scase(n);
//        }
    }

    static boolean isTr(long a, long b, long c) {
        if(a == b || a == c || b == c) {
            return false;
        }
        if (a + b <= c || a + c <= b || b + c <= a)
            return false;
        else
            return true;
    }


    static void solveCase(int t, int x, String s) {

    }

    static void scase(int[] arr1, int[] arr2) {
    }



    public static void main(String[] args) {
        solve();
    }


    static class LoggerNode {
        String message;
        int ts;
    }


    static class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }

    static class ListNode {
        int val;
        ListNode next;

        ListNode() {
        }

        ListNode(int val) {
            this.val = val;
        }

        ListNode(int val, ListNode next) {
            this.val = val;
            this.next = next;
        }
    }
}