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.

Examples

Input

6 2 4


Output

2


Input

7 4 3


Output

1


Input

10 1 2


Output

8


Input

1000000000000000 1000000000000000 1000000000000000


Output

1000000000000000
input = raw_input

x, k, d = map(int, input().split(" "))
is_plus = x >= 0
x = abs(x)

r = x // d
if r > k:
    y = x - k*d
else:
    y1 = x - r*d
    y2 = x - (r+1)*d
    k2 = k-r
    if k2 % 2 == 0:
        y = y1
    else:
        y = y2

y = abs(y)
print(y)