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 OCaml (4.02.3) (judge verdict: Memory Limit Exceeded)

let get_2_ints () = Scanf.scanf "%d %d" (fun u v -> u,v)

module Rep = struct
	let __range ?(stride=1) u v =
    let rec f0 i a = if i>v then a else f0 (i+stride) (i::a)
    in f0 u []
  let __ls_product l r =
    List.map (fun u -> List.map (fun v -> u,v) r) l
    |> List.concat
	let init f = f ()
  let rep ?(stride=1) f t = __range ~stride f t
	let (=+>) v p = (v,p)
	let (=>) (v,p) q = (v,__ls_product p q)
	let (=>>) (v,p) f = List.fold_left f v p
end

let () =
  let (n,y) = get_2_ints ()
  in let open Rep
  in init (fun () -> (-1,-1,-1))
  =+> rep 0 n => rep 0 n =>>
  (fun op (u,v) ->
    let w = n-u-v in
    if w>=0 && u*10000+v*5000+w*1000=y then (u,v,w) else op)
  |> (fun (u,v,w) -> Printf.printf "%d %d %d\n" u v w)