Final Ranking

Hongjun is a math teacher at a high school. $n$ students took the final exam, and a student with a higher score is ranked higher.

Grading is finished, but Hongjun only tells the students two facts.

• The sum of every student's score is $p$.
• Looking at the scores of the top $k$ ranked students, the number of distinct scores is exactly $d$.

Each score is a non-negative integer, and when the students are listed from the highest rank to the lowest the scores are non-increasing (equal scores are allowed). Reconstruct a score list consistent with this information.

Because several lists may satisfy the constraints, output the one that is lexicographically greatest when read from the highest-ranked student. That is, make the score of rank $1$ as large as possible, then the score of rank $2$ as large as possible, and so on.

The first line contains four space-separated integers $n$, $p$, $k$, $d$.

• $1 \le k \le n \le 1000$
• $0 \le p \le 1{,}000{,}000$
• $1 \le d \le k$

Print the lexicographically greatest valid score list, one score per line, from the highest-ranked student to the lowest.

If no score list can be built from the given values, print "Wrong information".