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: Wrong Answer)

"use strict"
const create = () => {
    const input = require("fs").readFileSync("/dev/stdin", "utf8").trim().split("\n");
    const res = {
        "list": input, "index": 0, "max": input.length,
        "hasNext": function () { return this.index < this.max },
        "next": function () { if (!this.hasNext()) { throw "ArrayIndexOutOfBoundsException"; } else { return this.list[this.index++]; } }
    };
    return res;
}
const o = create();
const next = () => o.next()
const nextInt = () => parseInt(o.next())
const nextStrArray = () => o.next().split(" ")
const nextIntArray = () => o.next().split(" ").map(el => parseInt(el))
const nextCharArray = () => o.next().split("")
const hasNext = () => o.hasNext()
const myout = (...x) => console.log(...x)
const Main = () => {
    let [x, k, d] = next().split(" ")
    let xx = BigInt(x)
    xx = xx > 0 ? xx : -1n * xx
    let kk = BigInt(k)
    let dd = BigInt(d)
    let div = xx / dd
    let ans
    if (div >= kk) {
        ans = xx - kk * dd
    } else {
        let rem = xx % dd
        let opp = rem - dd
        if (rem < -1n*opp && div % 2n != 0n) {
            ans = -1n*opp
        } else if(rem < -1n*opp && div % 2n == 0n) {
            ans = rem
        } else if(rem >= -1n*opp && div % 2n != 0n) {
            ans = -1n*opp
        } else {
            ans = rem
        }
    }
    console.log(String(ans))

}
Main()