Problem:
Score : 300 points

Problem Statement

Given any integer x, Aoki can do the operation below.

Operation: Replace x with the absolute difference of x and K.

You are given the initial value of an integer N. Find the minimum possible value taken by N after Aoki does the operation zero or more times.

Constraints

0 ≤ N ≤ 10^{18}

1 ≤ K ≤ 10^{18}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the minimum possible value taken by N after Aoki does the operation zero or more times.

Sample Input 1

7 4

Sample Output 1

1

Initially, N=7.

After one operation, N becomes |7-4| = 3.

After two operations, N becomes |3-4| = 1, which is the minimum value taken by N.

Sample Input 2

2 6

Sample Output 2

2

N=2 after zero operations is the minimum.

Sample Input 3

1000000000000000000 1

Sample Output 3

0

Solution in C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <cstdio>
#include <iostream>

using namespace std;

int main()
{
  long int N, K;
  cin >> N;
  cin >> K;

  long int prev = N;
  long int curr = N - K;
  long int curr_abs = abs(curr);

  if (!(N % K))
  {
    cout << 0 << endl;
    return 0;
  }

  while (1)
  {
    if (!prev)
    {
      cout << prev << endl;
      return 0;
    }
    else if (!curr)
    {
      cout << curr << endl;
      return 0;
    }
    else if (prev < curr_abs && curr < 0)
    {
      cout << prev << endl;
      return 0;
    }
    else if (curr_abs < prev && curr <= 0)
    {
      cout << curr_abs << endl;
      return 0;
    }
    prev = curr_abs;
    curr -= K;
    curr_abs = abs(curr);
  }

  return 0;
}