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: Time Limit Exceeded)

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

if K == 1:
    print(min(abs(X-D),abs(X+D)))
elif K == 2:
    print(min(abs(X+D+D),abs(X-D-D),abs(X)))
elif K == 3:
    print(min(abs(X+D+D+D),abs(X+D),abs(X-D),abs(X-D-D-D)))
else:
    for i in range(3):
        if abs(X - D) >= abs(X+D):
            List.append(abs(X+D))
            X = X+D
        else:
            List.append(abs(X-D))
            X = X-D

    for i in range(K-3):
        if List[i] == List[i+2]:
            if K%2 == i%2:
                print(List[i+1])
            else:
                print(List[i])
            break
        else:
            if abs(X - D) >= abs(X+D):
                List.append(abs(X+D))
                X = X+D
            else:
                List.append(abs(X-D))
                X = X-D

    if len(List) == K:
        print(List[K-1])
    else:
        pass