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: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
//if(strcmp(s[i],"AC")==0)
//if(s[l]=='#')
/*小文字判定
if((moji>= 'a') && (moji<='z')){
    printf("a\n");
    return 0;
  }
  */

int W_Length(char *str){
	int length = 0;
	while(*str++ != '\0')
		length++;
	return length;
}

void swap(int *a, int *b){
  int temp;
  temp=*a;
  *a=*b;
  *b=temp;
}
//swap(&a, &b)

double deg(double theta){//deg to theta
return theta*(2*3.14159265359)/360;
}

int cmp( const void *p, const void *q ) {
    return *(int*)p - *(int*)q;
}//ちいさい順
//qsort(a,n,sizeof(int),cmp);
//char s[n][11]

int cmp_s(const void * left, const void * right)
{
	char *left_char = (char *)left;
  char *right_char = (char *)right;
  return strcmp(left_char, right_char);
}
//qsort(s,n,sizeof(s[0]),cmp_s);


int main (void)
{
	long long int a,k,d,b,c,n,i,x,temp;
  char s[200005];

scanf("%lld %lld %lld",&x,&k,&d);
  //printf("x=%lld, k=%lld, d=%lld",x,k,d);
  if(x<=-1){
  x=-x;
  }
  
    temp=x/d;
  if(x>d){
    if(temp>=k){
      
      if(x-k*d<0){
    printf("%lld\n",-x+k*d);
      return 0;
    }
      
    printf("%lld\n",x-k*d);
      return 0;
    }
  }
  
    k=k-temp;
  
  if(k%2==0){
    if(x-d*temp<0){
    printf("%lld\n",-x+d*temp);
      return 0;
    }
  printf("%lld\n",x-d*temp);
    return 0;
  }
  else{
    if(d*(temp+1)-x<0){
    printf("%lld\n",-d*(temp+1)+x);
      return 0;
    }
  printf("%lld\n",d*(temp+1)-x);
    //printf("k=%lld, temp=%lld, x=%lld",k,temp,x);
    return 0;
  }
	
return 0;
}