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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

list = list(map(int, input().split())) 
hajime=list[0]
kaisuu=list[1]
hohaba=list[2]
if hajime>=0:
  ayumi=hajime//hohaba
  nokori=kaisuu-ayumi
  kouho_1=hajime-hohaba*kaisuu
  kouho_2=hajime-hohaba*ayumi
  kouho_3=hajime-hohaba*(ayumi+1)
 
  
  
  if kaisuu <= ayumi:
    print(kouho_1)
  else:
    if nokori%2==0:
      print(kouho_2)
    else:
      print(-kouho_3)
      
if hajime<0:  
  a=-hajime
  ayumi=a//hohaba
  nokori=kaisuu-ayumi
  kouho_1=hajime+hohaba*kaisuu
  kouho_2=hajime+hohaba*ayumi
  kouho_3=hajime+hohaba*(ayumi+1)
  if kaisuu<=hohaba:
    
    print(-kouho_1)  
  else:
    if nokori%2==0:
      print(-kouho_2)
    else:
      print(kouho_3)