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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.List
import qualified Data.IntMap as M
import Data.Maybe(fromJust)

main = do
  [n,y] <- map read . words <$> getLine :: IO [Int]
  let patten = [(i, j) | i <- [0..n], j <- [0..n-i]]
      m = foldl (solve n y) M.empty patten
      ans = M.lookup y m
  if ans /= Nothing
    then let (a, b) = fromJust ans
         in putStrLn $ show a ++ " " ++ show b ++ " " ++ show (n-a-b)
    else putStrLn "-1 -1 -1"

solve :: Int -> Int -> M.IntMap (Int, Int) -> (Int, Int) -> M.IntMap (Int, Int)
solve n y m (i, j) = M.insert (i*10000+j*5000+(n-i-j)*1000) (i, j) m