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)

main :: IO ()
main = do
    line <- getLine
    let n = read (head (splitOn ' ' line)) :: Int
    let y = read (last (splitOn ' ' line)) :: Int
    putStrLn $ showRes $ calc n y

calc :: Int -> Int -> (Int, Int, Int)
calc n y = if length res == 0 then (-1, -1, -1) else snd $ head res
    where
        res = filter (\x -> y == fst x) $ map calcSum [(a, b, n - a - b) | a <- [0..n], b <- [0..(n - a)]]
        calcSum (a, b, c) = (a * 10000 + b * 5000 + c * 1000, (a, b, c))

showRes :: (Int, Int, Int) -> String
showRes (a, b, c) = show a ++ " " ++ show b ++ " " ++ show c

splitOn :: Char -> String -> [String]
splitOn c s
    = current "" [] c $ reverse s
    where
        current :: String -> [String] -> Char -> String -> [String]
        current cur lis c [] = cur:lis
        current cur lis c (x:ss)
            = if c == x then
                  current "" (cur:lis) c ss
              else
                  current (x:cur) lis c ss