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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

fun main(args:Array<String>) {
    val (n,y) = readLine()!!.split(" ").map { it.toInt() }
    val ans = getAns(n,y)
    if(ans.isEmpty()) {
        println("-1 -1 -1")
    } else {
        print(ans.joinToString(" "))
    }
}

val dic = mutableMapOf<Int, MutableMap<Int, List<Int>>>()

fun getAns(remain:Int, amount:Int):List<Int> {
    if(remain <= 0) {
        if(amount == 0) {
            return listOf(0,0,0)
        } else {
            return listOf()
        }
    }
    if(amount <= 0) {
        return listOf()
    }
    if(amount > remain * 10000) {
        return listOf()
    }
    if(amount < remain * 1000) {
        return listOf()
    }
    if(!dic.containsKey(remain)) {
        dic[remain] = mutableMapOf()
    }
    dic[remain]!![amount]?.let { return it }

    var ans = mutableListOf<Int>()
    for(i in Math.min(amount/10000, remain) downTo 1) {
        val ret = getAns(remain-i, amount - (i*10000))
        if(ret.isNotEmpty()) {
            ans = ret.toMutableList()
            ans[0] += i
            break
        }
    }
    if(ans.isEmpty()) {
        for(i in Math.min(amount/5000, remain) downTo 1) {
            val ret = getAns(remain-i, amount-(i*5000))
            if(ret.isNotEmpty()) {
                ans = ret.toMutableList()
                ans[1] += i
                break
            }
        }
    }
    if(ans.isEmpty()) {
        for (i in Math.min(amount/1000, remain) downTo 1) {
            val ret = getAns(remain-i, amount-(i*1000))
            if(ret.isNotEmpty()) {
                ans = ret.toMutableList()
                ans[2] += i
                break
            }
        }
    }
    dic[remain]!![amount] = ans
    return ans
}