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 JavaScript (Node.js 12.16.1) (judge verdict: Accepted)

"use strict";
    
const main = arg => {
    arg = arg.trim().split("\n");
    let X = parseInt(arg[0].split(" ")[0]);
    const K = parseInt(arg[0].split(" ")[1]);
    const D = parseInt(arg[0].split(" ")[2]);
    
    let answer = 0;
    
    X = Math.abs(X);
    
    // if(X >= 0) {
        // 0までたどり着かない
        if(X - (K * D) > 0) {
            answer = X - (K * D);
            console.log(answer);
            return;
        // 0までたどり着く
        } else {
            let rest = K - Math.ceil(X / D);
            let now = X - (D * Math.ceil(X / D));
            // console.log(Math.ceil(X / D));
            // console.log(now);

            if(rest % 2 !== 0) {
                now += D; 
            }
            
            console.log(Math.abs(now));
        }
    // }
}
main(require('fs').readFileSync('/dev/stdin', 'utf8'));