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

inp = list(map(int,raw_input().split()))
x = inp[0]
k = inp[1]
d = inp[2]
x = abs(x)
if(x >= k*d):
    print(x-k*d)
else:
    res=10000000000000000000000000000000000000
    tmp = int(x/d)
    for y in range(-100,100):
        if((y+tmp)<=k and y+tmp >=0):
            rem = k-y-tmp
            if(rem%2 == 0):
                res=min(res,abs(x-(y+tmp)*d))
    print(res)
