The Football Season

Description:

Input:

The first line contains four integers $$$n$$$, $$$p$$$, $$$w$$$ and $$$d$$$ $$$(1 \le n \le 10^{12}, 0 \le p \le 10^{17}, 1 \le d < w \le 10^{5})$$$ — the number of games, the number of points the team got, the number of points awarded for winning a match, and the number of points awarded for a draw, respectively. Note that $$$w > d$$$, so the number of points awarded for winning is strictly greater than the number of points awarded for draw.

Output:

If there is no answer, print $$$-1$$$.

Otherwise print three non-negative integers $$$x$$$, $$$y$$$ and $$$z$$$ — the number of wins, draws and losses of the team. If there are multiple possible triples $$$(x, y, z)$$$, print any of them. The numbers should meet the following conditions:

• $$$x \cdot w + y \cdot d = p$$$,
• $$$x + y + z = n$$$.

Sample Input:

30 60 3 1

Sample Output:

17 9 4

Sample Input:

10 51 5 4

Sample Output:

-1

Sample Input:

20 0 15 5

Sample Output:

0 0 20

Note:

One of the possible answers in the first example — $$$17$$$ wins, $$$9$$$ draws and $$$4$$$ losses. Then the team got $$$17 \cdot 3 + 9 \cdot 1 = 60$$$ points in $$$17 + 9 + 4 = 30$$$ games.

In the second example the maximum possible score is $$$10 \cdot 5 = 50$$$. Since $$$p = 51$$$, there is no answer.

In the third example the team got $$$0$$$ points, so all $$$20$$$ games were lost.