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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System.Collections;
using System.Text;
using System.Threading.Tasks;
using static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System;
using System.Numerics;

class Program
{
    static void Main()
    {
        long[] NK = ReadLongs;
        long N = NK[0];
        long K = NK[1];

        N %= K;



        WriteLine(Min(N,K-N));




        ReadLine();
    }

  


    public static long GetInv(long a, long mod)
    {
        return PowerMod(a, mod - 2, mod);
    }
    public static long Combination(long a, long b, long mod)
    {
        if (b < 0 || b > a) return 0;
        if (b > a / 2) b = a - b;
        long numerator = Factorial(a, mod);
        long denominator = (Factorial(b, mod) * Factorial(a - b, mod)) % mod;

        return (numerator * GetInv(denominator, mod)) % mod;
    }
    public static long Factorial(long n, long mod)
    {
        if (n == 0) return 1;
        if (n == 1) return 1;
        long ans = n;
        for (int i = 2; i < n; i++)
        {
            ans = (ans * i) % mod;
        }

        return ans;
    }
    private static long PowerMod(long a, long n, long mod)
    {
        if (n == 1) return a;

        long p = PowerMod(a, n / 2, mod);
        if (n % 2 == 1) return ((p * p) % mod * a) % mod;
        else return (p * p) % mod;
    }


    struct Vector2Int
    {
        public Vector2Int(int x, int y)
        {
            X = x;
            Y = y;
        }
        public int X;
        public int Y;
        public double Magnitude => Math.Sqrt(X * X + Y * Y);

        public static Vector2Int zero => new Vector2Int(0, 0);
        public static Vector2Int u => new Vector2Int(0, 1);
        public static Vector2Int r => new Vector2Int(1, 0);
        public static Vector2Int d => new Vector2Int(0, -1);
        public static Vector2Int l => new Vector2Int(-1, 0);
        public static Vector2Int[] AllDirections => new Vector2Int[4] { u, r, d, l };
        public static Vector2Int[] AllDirections8 => new Vector2Int[8] { u, r, d, l, u + r, r + d, d + l, l + u };


        public static Vector2Int operator +(Vector2Int a, Vector2Int b)
        {
            return new Vector2Int(a.X + b.X, a.Y + b.Y);
        }
        public static Vector2Int operator -(Vector2Int a, Vector2Int b)
        {
            return new Vector2Int(a.X - b.X, a.Y - b.Y);
        }
        public static bool operator ==(Vector2Int a, Vector2Int b)
        {
            return a.X == b.X && a.Y == b.Y;
        }
        public static bool operator !=(Vector2Int a, Vector2Int b)
        {
            return a.X != b.X || a.Y != b.Y;
        }
        public static Vector2Int operator *(Vector2Int v, int n)
        {
            return new Vector2Int(v.X * n, v.Y * n);
        }
        public static Vector2Int operator *(int n, Vector2Int v)
        {
            return new Vector2Int(v.X * n, v.Y * n);
        }
    }
    struct Vector3Int
    {
        public Vector3Int(int x, int y, int z)
        {
            X = x;
            Y = y;
            Z = z;
        }
        public int X;
        public int Y;
        public int Z;

        public double Magnitude => Math.Sqrt(X * X + Y * Y + Z * Z);

        public static Vector3Int zero => new Vector3Int(0, 0, 0);
        public static Vector3Int u => new Vector3Int(0, 1, 0);
        public static Vector3Int r => new Vector3Int(1, 0, 0);
        public static Vector3Int d => new Vector3Int(0, -1, 0);
        public static Vector3Int l => new Vector3Int(-1, 0, 0);

        public static Vector3Int operator +(Vector3Int a, Vector3Int b)
        {
            return new Vector3Int(a.X + b.X, a.Y + b.Y, a.Z + b.Z);
        }
        public static Vector3Int operator -(Vector3Int a, Vector3Int b)
        {
            return new Vector3Int(a.X - b.X, a.Y - b.Y, a.Z - b.Z);
        }
        public static bool operator ==(Vector3Int a, Vector3Int b)
        {
            return a.X == b.X && a.Y == b.Y && a.Z == b.Z;
        }
        public static bool operator !=(Vector3Int a, Vector3Int b)
        {
            return a.X != b.X || a.Y != b.Y || a.Z != b.Z;
        }
        public static Vector3Int operator *(Vector3Int v, int n)
        {
            return new Vector3Int(v.X * n, v.Y * n, v.Z * n);
        }
        public static Vector3Int operator *(int n, Vector3Int v)
        {
            return new Vector3Int(v.X * n, v.Y * n, v.Z * n);
        }
    }

    #region Reader
    static Vector2Int ReadVec2Int
    {
        get
        {
            string[] s = Console.ReadLine().Split(' ');
            return new Vector2Int(int.Parse(s[0]), int.Parse(s[1]));
        }
    }
    static Vector2Int[] ReadVec2Ints(int n)
    {
        List<Vector2Int> list = new List<Vector2Int>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadInts;
            list.Add(new Vector2Int(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static HashSet<Vector2Int> ReadVec2IntHash(int n)
    {
        HashSet<Vector2Int> hash = new HashSet<Vector2Int>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadInts;
            hash.Add(new Vector2Int(ab[0], ab[1]));
        }
        return hash;
    }
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine());
    static int[] ReadInts => Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReadLong => Convert.ToInt64(Console.ReadLine());
    static long[] ReadLongs => Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    static long[,] ReLongMatrix(int r, int c)
    {
        var mat = new long[r, c];
        for (int i = 0; i < r; ++i)
        {
            var x = ReadLongs;
            for (int j = 0; j < c; ++j)
            {
                mat[i, j] = x[j];
            }
        }
        return mat;
    }
    static Tuple<string, string>[] ReTupleStr(int n)
    {
        List<Tuple<string, string>> list = new List<Tuple<string, string>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadStrs;
            list.Add(new Tuple<string, string>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<long, long>[] ReTupleLong(int n)
    {
        List<Tuple<long, long>> list = new List<Tuple<long, long>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongs;
            list.Add(new Tuple<long, long>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<int, int>[] ReadTupleInt(int n)
    {
        List<Tuple<int, int>> list = new List<Tuple<int, int>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadInts;
            list.Add(new Tuple<int, int>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Tuple<double, double>[] ReTupleDouble(int n)
    {
        List<Tuple<double, double>> list = new List<Tuple<double, double>>();
        for (int i = 0; i < n; ++i)
        {
            var ab = ReadLongs;
            list.Add(new Tuple<double, double>(ab[0], ab[1]));
        }
        return list.ToArray();
    }
    static Dictionary<int, HashSet<int>> ReAdjacencyList(int N, int M)
    {
        Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
        for (int i = 0; i <= N; ++i)
        {
            dict.Add(i, new HashSet<int>());
        }
        for (int i = 0; i < M; ++i)
        {
            var ab = ReadInts;
            dict[ab[0]].Add(ab[1]);
            dict[ab[1]].Add(ab[0]);
        }
        return dict;
    }
    #endregion
    static void Swap<T>(ref T a,ref T b)
    {
        T temp = a;
        a = b;
        b = temp;
    }

    static long mod = (int)Pow(10, 9) + 7;

}