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: Wrong Answer)

x,k,d = [int(x) for x in input().split()]
t = abs(int(x/d))
if x < 0:
    d = -d
if t >= k:
    print(x-d*k)
elif t == 0:
    if k % 2 == 0:
        print(abs(x))
    else:
        print(min(abs(x-d),abs(x+d)))
elif t < k:
    if abs(x-d*t) < abs(x-d*t-d):
        if (t-k)%2==0:
            print(abs(x-d*t))
        else:
            print(min(abs(x-d*t+d),abs(x-d*t-d)))
    elif abs(x-d*t) == abs(x-d*t-d):
        print(abs(x-d*t))
    else:
        if (t-k-1)%2==0:
            print(abs(x-d*t-d))
        else:
            print(min(abs(x-d*t),abs(x-d*t-2*d)))