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 Python (3.8.2) (judge verdict: Accepted)

N,Y = map(int,input().split())
a,b,c = N+1,N+1,N+1
dama = 0
count = 0

if Y // N == 10000:
    print(N,0,0)
elif Y // N == 5000:
    print(0,N,0)
elif Y // N == 1000:
    print(0,0,N)
else:
    stop = False
    for i in range(a):
        if stop:
            break
        b -= i
        for j in range(b):
            if stop:
                break
            c -= i+j
            if i+j+c != N:
                pass
            else:
                dama = 10000*i + 5000*j + 1000*c
                if dama == Y:
                    print(i,j,c)
                    count += 1
                    stop = True
                    break
            c = N
        b = N+1
    if count == 0:
        print(-1,-1,-1)