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: Accepted)

a,b,c=map(int,input().split())
a1=(abs(a)-0)%c
if(a==0):
    if(b%2==0):
        print(0)
    else:
        print(c)
if(a>0):
    a2=a1-c
    ma1=int(a/c)
    ma2=ma1+1
    a3=abs(a2)
    if(b>=ma2 and b>ma1):
        if((b-ma1)%2==0):
            print(a1)
        else:
            print(abs(a2))
    if(b==ma1):
        print(a1)
    if(b<ma1):
        print(a-(b*c))
if(a<0):
    a2=abs(a1-c)
    ma1=((a1-(2*a1))-(a))
    ma1=int(ma1/c)
    ma2=ma1+1
    if(b>=ma2 and b>ma1):
        if((b-ma1)%2==0):
            print(a1)
        else:
            print(abs(a2))
    if(b==ma1):
        print(a1)
    if(b<ma1):
        print(abs(a+(b*c)))