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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(let* ((n (read))
       (m (read))
       (x 0)
       (y 0)
       (z (floor m 1000)))
  (defun f-5000 ()
    (cond ((= (+ x y z) n) t)
          ((or (> 5 (- n x y z)) (minusp (- z 5))) nil)
          (t (progn (incf y) (setq z (- z 5)) (f-5000)))))
  (defun f-10000 ()
    (cond ((= (+ x y z) n) t)
          ((or (not (> 10 (- n x y z))) (not (minusp (- z 10)))) (progn (incf x) (setq z (- z 10)) (f-10000)))
          ((or (not (> 2 (- n x y z))) (not (minusp (- y 2)))) (progn (incf x) (setq y (- z 2)) (f-10000)))
          (t nil)))

  (if (or (not (< (* n 1000) m (* n 10000))) (not (= 0 (mod m 1000))))
      (setf x -1 y -1 z -1)
      (progn (f-5000) (f-10000)))
  (format t "~A ~A ~A" x y z ))