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 Python (3.8.2) (judge verdict: Accepted)

X, K, D = input().split()
X, K, D = int(X), int(K), int(D)
count = 0
if X < 0:
  X = -X
  L = X
else:
  L = X
if K < L // D:
  L = L - K * D
  K = 0
elif K == L // D:
#  print("koko")
  L = L % D
  K = 0
else:
#  print("C")
  temp = L
  L = L % D - D
  K = K - temp // D - 1
if L == 0:
  if K % 2 == 0:
    print(0)
    exit()
  else:
    print(D)
    exit()
if K == 0:
  print(abs(L))
  exit()
if abs(L) >= L + D:
  goal = L + D
  if K % 2 != 0:
    print(goal)
    exit()
  else:
    print(abs(L))
    exit()
elif abs(L) < L + D:
  goal = abs(L)
  if K % 2 == 0:
    print(abs(L))
    exit()
  else:
    print(L + D)
    exit()