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:
def check(n,y):
  if (y%1000!=0):
    return (-1, -1, -1)
  nn = y/1000
  nover = nn-n
  if (nover<0):
    return (-1, -1, -1)
  aend = nover/4 if(nover%4==0) else nover/4+1
  for a in range(int(nover/4)+1):
    if (((nover-a*4)>=0) and (nover-a*4)%9==0):
      nh = a
      ny = (nover-4*a)/9
      nn = nn - 5*nh - 10*ny
      if(nn<0):
        return (-1, -1, -1)
      return (ny,nh,nn)
  return (-1, -1, -1)


if __name__=='__main__':
  n, y = map(int, raw_input().split())
  ny, nh, nn = check(n,y)
  print ny, nh, nn