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)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines


x, k, d = map(int, readline().split())
# x, k, d = (10, 31, 3)
if x < 0 and x + (k * d) < 0:
    print(x + (k * d))
    exit()
elif x >= 0 and x - (k * d) >= 0:
    print(x - (k * d))
    exit()

a = abs(x // d)
# print(a)
if k % 2 == 0:
    if a % 2 != 0:
        i = (a - 1)*d
        j = (a + 1)*d
    else:
        i = a * d
        j = 0
else:
    if a % 2 != 0:
        i = a * d
        j = 0
    else:
        i = (a - 1)*d
        j = (a + 1)*d
# a *= d
# print(a)
if x < 0:
    print(min(abs(x+i), abs(x+j)))
else:
    print(min(abs(x-i), abs(x-j)))