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 <stdlib.h>
#include <math.h>
#include <string.h>
 
 
void swap (int *x, int *y) {
  int temp;    
 
  temp = *x;
  *x = *y;
  *y = temp;
}
 
int gcd(int a,int b){
  if(a<b){
    swap(&a,&b);
  }
 
  if(b==0){
    return a;
  }
 
  int r=a%b;
  while(r!=0){
    a = b;
    b = r;
    r = (a%b);
  }
 
  return b;
}
 
/* クイックソート */
int dn(const void*a,const void*b){return*(int*)b-*(int*)a;}
 
 
int modpow(int a,int n,int mod){
  int ans=1;
  while(n>0){
    if(n & 1){
      ans=ans*a%mod;
    }
    a=a*a%mod;
    n/=2;
  }
  return ans;
}
 
int max(int a,int b){
  if(a<b){
    return b;
  }
  else{
    return a;
  }
}
 
int min(int a,int b){
  if(a<b){
    return a;
  }
  else{
    return b;
  }
}
 
void chmax(int *a,int b){
  if(*a < b){
    *a = b;
  }
 
  return;
}
 
void chmin(int *a,int b){
  if(*a > b){
    *a =b;
  }
 
  return;
}
 

int main(void){
  long int x,k,d;
  scanf("%ld%ld%ld",&x,&k,&d);
  long int len;
  if(x<0){
    len=-x;
  }else{
    len=x;
  }
  long int mvc=len/d;
  long int mod=len%d;
  long int dif=len-d*mvc;
  if(len==d && k%2==0){
    printf("%ld\n",len);
    return 0;
  }
  if(len==d && k%2==1){
    printf("0\n");
    return 0;
  }
  if(len<d){
    if(d<2*len && k%2==1){
      printf("%ld\n",mvc*d-len);
      return 0;
    }else if(d<2*len && k%2==0){
      printf("%ld\n",len);
      return 0;
    }else if(2*len<d){
      printf("%ld\n",len);
      return 0;
    }
  }
  if(k<mvc){
    printf("%ld\n",len-k*d);
    return 0;
  }else{
    if((k-mvc)%2==1){
      printf("%ld\n",(mvc+1)*d-len);
      return 0;
    }else{
      printf("%ld\n",len-mvc*d);
      return 0;
    }
  }
}