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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

import math

x, k, d = map(int, input().split())
left = 0
right =k
while(left<right):
    mid = (left+right)//2
    if(x-(d*mid)<0):
        right = mid
    else:
        left = mid+1
low= left
high = left-1
v1 = abs(x-(low*d))
v2 = abs(x-(high*d))
if(k%2==0):
    if(v1<=v2):
        if(low%2==0):
            print(v1)
        else:
            print(v2)
    else:
        if(high%2==0):
            print(v2)
        else:
            print(v1)
else:
    if(v1<=v2):
        if(low%2==1):
            print(v1)
        else:
            print(v2)
    else:
        if(high%2==1):
            print(v2)
        else:
            print(v1)