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: Runtime Error)

if K <= 0:
    list_ = [abs((X - K * D) + (2* i * D)) for i in list(range(0,K+1))]
    result = min(list_)
    print(result)
    

else:
    
    it = int(K /2)
    tmp_result = abs((X - K * D) + (2* (it +1) * D))
    
    flag =True
    
    while flag:
        
        if it == 0:
            result = abs((X - K * D) + (2* 0 * D))
            flag = False
            
        elif it == (K+1):
            result = abs((X - K * D) + (2* (K+1) * D))
            flag = False
        
        
        
        result = abs((X - K * D) + (2* it * D)) 
        result_m = abs((X - K * D) + (2* (it -1) * D))
        result_p = abs((X - K * D) + (2* (it +1) * D))
        
        if result <= result_m and result <= result_p:
            flag =False
            
        if result > result_m:
            if it == 4:
                it = 3
            elif it == 3:
                it = 2
            elif it == 2:
                it =1
            elif it ==1:
                it = 0
            else:
                it = int(it/2)
                
        elif result > result_p:
            if (K+1- it) == 4:
                it = K-2
            elif (K+1- it) == 3:
                it = K-1
            elif (K+1- it) == 2:
                it =K
            elif (K+1- it) ==1:
                it = K+1
            else:
                it = it +(int((K+1- it)/2))
    print(result)