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)

X,K,D = [int(a) for a in input().split()]
X0=X
u=max(abs(X),D)
l=-u
now=0
for i in range(K):
    if i==0:
        if X>0 and X-K*D>0:
            print(X-K*D)
            break
        if X<0 and X+K+D<0:
            print(X+K*D)
            break
    if X>0:X-=D
    elif X<=0:X+=D
    if X>0 and X<X0:
        u=X
        now=1
    if X<0 and X>-X0:
        l=X
        now=-1
    if X==abs(X0):
        u=X
        if i!=K-1:l=0
        now=1
    if X==-abs(X0):
        l=X
        if i!=K-1:u=0
        now=-1
    #print(X,u,l,i,now)
    if X==0 and i==K-1:
        print("0")
        break
    if (u>0 and u<X0 and l<0 and l>-X0) or (u==0 or l==0):
        if (K-1-i)%2==0:
            if now==1:
                print(u)
            else:
                print(abs(l))
        else:
            if now==1:
                print(abs(l))
            else:
                print(u)
        break
    if i==K-1:
        print(abs(X))