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)

#n, m, q = map(int, input().split())
#List = list(map(int, input().split()))
#req = [list(map(int, input().split())) for _ in range(q)]
#t = t[:-1]
#print(ans[j], end = "") 改行無しで出力
#[0]*n
#sort = sorted(a)[::-1] 降順
import math
x, k, d = map(int, input().split())

num = k*d

x = abs(x)
flag = 0

if x >= num:
    print(x - num)
else:
    if x > d:
        j = int(x / d)
    else:
        if x*2 > d:
            j = 1
            flag = 1
        else:
            j = 0

    if j == 0:
        b = x
    elif j == 1 and flag == 1:
        b = d - x
    else:
        b = x % (d*j)
    min = min(b, d - b)
    max = max(b, d - b)
    if min == d - b:
        j += 1

    if (k - j) % 2 == 0:
        print(min)
    else:
        print(max)