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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

#! /usr/bin/perl

use strict;
use warnings;

chomp(my $buf = <>);
my($count, $total) = split(/\s+/, $buf);

xxx($total - $count * 1000, $count, 0, 0);
print "-1 -1 -1\n";

sub xxx {
    my($remain, $c1k, $c5k, $c10k) = @_;

    if($remain == 0) {
        print "$c10k $c5k $c1k\n";
        exit;
    }
    if($remain < 0) {
        print "-1 -1 -1\n";
        exit;
    }
    if(4000 <= $remain && 0 < $c1k) {
        xxx($remain - 4000, $c1k-1, $c5k+1, $c10k);
    }
    if(9000 <= $remain && 0 < $c1k) {
        my($tmpRemain, $tmpC1k, $tmpC10k) = ($remain, $c1k, $c10k);
        while(9000 <= $tmpRemain && 0 < $tmpC1k){
            $tmpRemain -= 9000;
            $tmpC1k --;
            $tmpC10k ++;
        }
        xxx($tmpRemain, $tmpC1k, $c5k, $tmpC10k);
    }
    if(5000 <= $remain && 0 < $c5k) {
        my($tmpRemain, $tmpC5k, $tmpC10k) = ($remain, $c5k, $c10k);
        while(5000 <= $tmpRemain && 0 < $tmpC5k){
            $tmpRemain -= 5000;
            $tmpC5k --;
            $tmpC10k ++;
        }
        xxx($tmpRemain, $c1k, $tmpC5k, $tmpC10k);
    }
}