Problem: 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.

Examples

Input

9 45000


Output

4 0 5


Input

20 196000


Output

-1 -1 -1


Input

1000 1234000


Output

14 27 959


Input

2000 20000000


Output

2000 0 0

Solution (in PYTHON):

Solution:
N, Y = map(int, raw_input().split())

if Y == N * 10000:
    print " ".join(map(str, [N, 0, 0]))
elif Y > N * 10000:
    print " ".join(map(str, [-1, -1, -1]))
elif Y < N * 1000:
    print " ".join(map(str, [-1, -1, -1]))
elif Y == N * 1000:
    print " ".join(map(str, [0, 0, N]))


else:
    dif = N * 10000 - Y

    ext = dif % 9000
    if ext == 0:
        noguchi = dif / 9000
        print " ".join(map(str, [N-noguchi, 0, noguchi]))
    else:
        if ext == 1000:
            higuchi = 2
        elif ext == 2000:
            higuchi = 4
        elif ext == 3000:
            higuchi = 6
        elif ext == 4000:
            higuchi = 8
        elif ext == 5000:
            higuchi = 1
        elif ext == 6000:
            higuchi = 3
        elif ext == 7000:
            higuchi = 5
        elif ext == 8000:
            higuchi = 7

        dif = ((N - higuchi) * 10000 + higuchi * 5000)- Y
        if dif < 0:
            print " ".join(map(str, [-1, -1, -1]))
        else:
            noguchi = dif / 9000
            yukichi = N - (noguchi + higuchi)

            if not noguchi < 0 and not higuchi < 0 and not yukichi < 0:
                print " ".join(map(str, [yukichi, higuchi, noguchi]))
            else:
                print " ".join(map(str, [-1, -1, -1]))