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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"fmt"
)

func main() {
	var n, y int
	fmt.Scanf("%d %d", &n, &y)

	// a, b, c := findPair(0, 0, 0, n, y)
	a, b, c := findPair2(n, y)
	fmt.Println(a, b, c)
}

func findPair2(n, y int) (int, int, int) {
	for i := 0; i <= n; i++ {
		for j := 0; j <= n-i; j++ {
			k := n - i - j
			if k >= 0 && i*10000+j*5000+k*1000 == y {
				return i, j, k
			}
		}
	}
	return -1, -1, -1
}

func findPair(a, b, c, n, y int) (int, int, int) {
	// fmt.Printf("a=%d, b=%d, c=%d, n=%d, y=%d\n", a, b, c, n, y)
	if y == 0 {
		if n == 0 {
			return a, b, c
		} else {
			return -1, -1, -1
		}
	} else if y < 0 {
		return -1, -1, -1
	}

	if n > 0 {
		if 10000*n < y {
			return -1, -1, -1
		}
		if r1, r2, r3 := findPair(a+1, b, c, n-1, y-10000); r1 != -1 {
			return r1, r2, r3
		}
		if 5000*n < y {
			return -1, -1, -1
		}
		if r1, r2, r3 := findPair(a, b+1, c, n-1, y-5000); r1 != -1 {
			return r1, r2, r3
		}
		if 1000*n < y {
			return -1, -1, -1
		}
		if r1, r2, r3 := findPair(a, b, c+1, n-1, y-1000); r1 != -1 {
			return r1, r2, r3
		}
	}
	return -1, -1, -1
}