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
l=list(map(int,raw_input().split()))
x=int(l[0])
k=int(l[1])
d=int(l[2])
s = 0
e = (k/2)

ans = int(1e32)

while s<=e :
    m = (s+e)/2
    curr = abs(x+(k-2*m)*d)
    ans = min(curr,ans)
    left = abs(x+(k-2*(m-1))*d)
    right = abs(x+(k-2*(m+1))*d)

    if(left < curr or right < curr):
        if(left<right):
            e=m-1
        else:
            s=m+1
    else:
        break 

s=0
e=(k/2)
ans2= int(1e32)
#negative
while s<=e :
    m = (s+e)/2
    curr = abs(x-(k-2*m)*d)
    ans2 = min(curr,ans2)
    left = abs(x-(k-2*(m-1))*d)
    right = abs(x-(k-2*(m+1))*d)

    if(left < curr or right < curr):
        if(left<right):
            e=m-1
        else: 
            s=m+1
    else:
        break 

ans = min(ans2,ans)

print(ans)


    
