Problem:
Score : 300 points

Problem Statement

The commonly used bills in Japan are 10000-yen, 5000-yen and 1000-yen bills. Below, the word "bill" refers to only these.

According to Aohashi, he received an otoshidama (New Year money gift) envelope from his grandfather that contained N bills for a total of Y yen, but he may be lying. Determine whether such a situation is possible, and if it is, find a possible set of bills contained in the envelope. Assume that his grandfather is rich enough, and the envelope was large enough.

Constraints

1 ≤ N ≤ 2000

1000 ≤ Y ≤ 2 × 10^7

N is an integer.

Y is a multiple of 1000.

Input

Input is given from Standard Input in the following format:

N Y

Output

If the total value of N bills cannot be Y yen, print -1 -1 -1.

If the total value of N bills can be Y yen, let one such set of bills be "x 10000-yen bills, y 5000-yen bills and z 1000-yen bills", and print x, y, z with spaces in between. If there are multiple possibilities, any of them may be printed.

Sample Input 1

9 45000

Sample Output 1

4 0 5

If the envelope contained 4 10000-yen bills and 5 1000-yen bills, he had 9 bills and 45000 yen in total. It is also possible that the envelope contained 9 5000-yen bills, so the output 0 9 0 is also correct.

Sample Input 2

20 196000

Sample Output 2

-1 -1 -1

When the envelope contained 20 bills in total, the total value would be 200000 yen if all the bills were 10000-yen bills, and would be at most 195000 yen otherwise, so it would never be 196000 yen.

Sample Input 3

1000 1234000

Sample Output 3

14 27 959

There are also many other possibilities.

Sample Input 4

2000 20000000

Sample Output 4

2000 0 0

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {

            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            //var N = line1[0];
            //var M = line1[1];
            //var a = new long[M];
            //var b = new long[M];

            //int bridge = 0;

            //int[,] dag = new int[N,N];

            //for (int i = 0; i < M; i++)
            //{
            //    var line2 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
            //    a[i] = line2[0]-1;
            //    b[i] = line2[1]-1;
            //    dag[a[i], b[i]] = 1;
            //    dag[b[i], a[i]] = 1;
            //}

            //for (int i = 0; i < M; i++)
            //{
            //    bool[] visited = new bool[N];
            //    dag[a[i], b[i]] = 0;
            //    dag[b[i], a[i]] = 0;
            //    DFS(0,visited,dag);

            //    if (visited.Where(n => n == true).Count() != N)
            //    {
            //        bridge++;
            //    }

            //    dag[a[i], b[i]] = 1;
            //    dag[b[i], a[i]] = 1;
            //}
            //Console.WriteLine(bridge);
            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);

            //var A = line1[0];
            //var B = line1[1];
            //var C = line1[2];
            //var D = line1[3];
            //var E = line1[4];
            //var F = line1[5];

            //var N = int.Parse(Console.ReadLine());
            //char[] mozi = new char[N];
            //long[] MARCH = new long[5];
            //long cnt = 0;


            //for (int i = 0; i < N; i++)
            //{
            //    mozi[i] = Console.ReadLine().ToCharArray()[0];
            //}

            //MARCH[0] = mozi.Where(n => n == 'M').Count();
            //MARCH[1] = mozi.Where(n => n == 'A').Count();
            //MARCH[2] = mozi.Where(n => n == 'R').Count();
            //MARCH[3] = mozi.Where(n => n == 'C').Count();
            //MARCH[4] = mozi.Where(n => n == 'H').Count();

            //for (int i = 0; i < 3; i++)
            //{
            //    for (int j = i + 1; j < 4; j++)
            //    {
            //        for (int k = j + 1; k < 5; k++)
            //        {
            //            cnt += MARCH[i] * MARCH[j] * MARCH[k];
            //        }
            //    }
            //}

            //Console.WriteLine(cnt);

            //var N = int.Parse(Console.ReadLine());

            //var line1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //var line2 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //int candy = 0;
            //int MAX = 0;

            //for (int i = 0; i < N; i++)
            //{
            //    for (int k = 0; k <= i; k++)
            //    {
            //        candy += line1[k];
            //    }

            //    for (int j = N - 1; j >= i; j--)
            //    {
            //        candy += line2[j];
            //    }

            //    MAX = Math.Max(candy,MAX);
            //    candy = 0;
            //}

            //Console.WriteLine(MAX);

            //var N = int.Parse(Console.ReadLine());
            //List<int[]> list = new List<int[]>();
            //int t = 0;
            //int x = 0;
            //int y = 0;

            //for (int i = 0; i < N; i++)
            //{
            //    var txy = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            //    list.Add(txy);
            //}

            //foreach (var item in list)
            //{
            //    if (item[0] - t >= Math.Abs(item[1] + item[2] - x - y))
            //    {

            //        if (((item[0] - t) % 2 == 1 && Math.Abs(x + y - item[1] - item[2]) % 2 == 1) ||
            //            ((item[0] - t) % 2 == 0 && Math.Abs(x + y - item[1] - item[2]) % 2 == 0))
            //        {
            //            t = item[0];
            //            x = item[1];
            //            y = item[2];
            //        }
            //        else
            //        {
            //            Console.WriteLine("No");
            //            return;
            //        }
            //    }
            //    else
            //    {
            //        Console.WriteLine("No");
            //        return;
            //    }
            //}

            //Console.WriteLine("Yes");

            var line1 = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);

            if (line1[1] > 10000)
            {
                for (int i = 0; i <= line1[1]/10000; i++)
                {
                    for (int j = 0; j <= line1[1] / 5000; j++)
                    {
                        if (10000 * i + 5000 * j + (line1[0] - i - j) * 1000 == line1[1] && line1[0] - i - j >= 0)
                        {
                            Console.WriteLine("{0} {1} {2}",i,j,line1[0] - i - j);
                            return;
                        }
                    }
                }
            }
            else
            {
                for (int i = 0; i < 2; i++)
                {
                    for (int j = 0; j <= 9; j++)
                    {
                        if (5000 * i + 1000 * j == line1[1] && i + j == line1[0])
                        {
                            Console.WriteLine("{0} {1} {2}", 0, i, j);
                            return;
                        }
                    }
                }
            }

            Console.WriteLine("{0} {1} {2}", -1, -1, -1);
        }

        public static void DFS(int v,bool[] visited,int[,] dag)
        {
            visited[v] = true;

            for (int i = 0; i < visited.Length; i++)
            {
                if (dag[v, i] == 0) continue;
                if (visited[i]) continue;
                DFS(i,visited,dag);
            }

        }

        public static long LowerBound<T>(T[] arr, long start, long end, T value, IComparer<T> comparer)
        {
            long low = start;
            long high = end;
            long mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static long LowerBound<T>(T[] arr, T value) where T : IComparable
        {
            return LowerBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }

        public static long UpperBound<T>(T[] arr, long start, long end, T value, IComparer<T> comparer)
        {
            long low = start;
            long high = end;
            long mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static long UpperBound<T>(T[] arr, T value)
        {
            return UpperBound(arr, 0, arr.Length, value, Comparer<T>.Default);
        }
    }

}