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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <math.h>

int main(){
    long X,K,D;
    long pre[3];
    scanf("%ld %ld %ld",&X,&K,&D);
    
    int x=X/D;
    if(x<K){
        if(X>0){
            X -= D*x;
        }else{
            X += D*x;
        }
        K-=x;
        //printf("-%d",x);
    }else{
        if(X>0){
            X -= D*K;
        }else{
            X += D*K;
        }
        K-=K;
        //printf("-%d",K);
    }

    for(long i=0;K>i;i++){
        if(X>0){
            X -= D;
        }else{
            X += D;
        }
        pre[2]=pre[1];
        pre[1]=pre[0];
        pre[0]=X;
        if(pre[0]==pre[2])
            break;
    }
    if(X<0)X*=-1;
    printf("%ld\n",X);
}