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)

X,K,D = map(int,input().split())

c = X

if c >= 0:
  if X < D:
    c = c - D
    if (K - 1) % 2 == 0:
      print(min(abs(X),abs(c)))
      exit()
    else:
      print(min(abs(c+D),abs(c-D)))
  elif X//D > K:
    c = c - D * K
    print(c)
    exit()
  else:
    c = c - D * (X//D)
    if (K - X//D) % 2 == 0:
      print(c)
      exit()
    else:
      print(min(abs(c+D),abs(c-D)))
else:
  if abs(X) < D:
    c = c + D
    if (K - 1) % 2 == 0:
      print(min(abs(X),abs(c)))
      exit()
    else:
      print(min(abs(c+D),abs(c-D)))
  elif abs(X)//D > K:
    c = c + D * K
    print(c)
    exit()
  else:
    c = c + D * (abs(X)//D)
    if (K - abs(X)//D) % 2 == 0:
      print(abs(c))
      exit()
    else:
      print(min(abs(c+D),abs(c-D)))