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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
// Context
class LieDetector
{
    public $algorithm = null;

    private $number_of_bills = 0;
    private $total_amount = 0;

    public function setElements()
    {
        $input = explode(" ", trim(fgets(STDIN)));
        $this->number_of_bills = $input[0];
        $this->total_amount = $input[1];
    }

    public function execLieDitect()
    {
        return $this->algorithm->lieDitect($this->number_of_bills, $this->total_amount);
    }
}

// Strategy
interface Algorithm
{
    public function lieDitect($number_of_bills, $total_amount);
}

// ConcreteStrategy
class tripleLoop implements Algorithm
{
    public function lieDitect($number_of_bills, $total_amount)
    {
        $number_of_10000_yen_bills = 0;
        $number_of_5000_yen_bills = 0;
        $number_of_1000_yen_bills = 0;

        for (
            $number_of_10000_yen_bills = $number_of_bills;
            $number_of_10000_yen_bills >= 0;
            $number_of_10000_yen_bills--
        ) {
            for (
                $number_of_5000_yen_bills = $number_of_bills - $number_of_10000_yen_bills;
                $number_of_5000_yen_bills >= 0;
                $number_of_5000_yen_bills--
            ) {
                $number_of_1000_yen_bills = $number_of_bills - ($number_of_10000_yen_bills + $number_of_5000_yen_bills);
                $sum_amount = 10000 * $number_of_10000_yen_bills + 5000 * $number_of_5000_yen_bills + 1000 * $number_of_1000_yen_bills;
                if ($sum_amount == $total_amount) {
                    return "${number_of_10000_yen_bills} ${number_of_5000_yen_bills} ${number_of_1000_yen_bills}";
                }
            }
        }
    }
}

// Main
$machine = new LieDetector();

$machine->algorithm = new tripleLoop();
$machine->setElements();
echo $machine->execLieDitect();