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)

# ####################################################################
# import io
# import sys

# _INPUT = """\
# 100 12 9
# """
# sys.stdin = io.StringIO(_INPUT)
####################################################################
####################################################################
import sys
def _p(*_a):
  #return
  _s=" ".join(map(str,_a))
  #print(_s)
  sys.stderr.write(_s+"\n")
####################################################################
def _pa(_aa):
  #return
  for _a in _aa: _p(_a)
####################################################################
X,K,D = map(int, input().split())

X = abs(X)

# K回移動しても、0に届かない場合
if K * D < X:
  ans = X - (K*D)
  print(ans)
  exit()


# 0に届く場合
a = X // D
k = K - a
x = X - (a * D)
# _p(a,k,x)
if k % 2 == 0:
  ans = x
else:
  ans = x - D

print(abs(ans))