Problem Description

Note: the notes in the score are numbers.

We define a subscore as a “non-empty contiguous sequence of notes”. That is, after sorting a sequence and removing duplicates, the difference between every two adjacent values is $1$.

For example, $(3,4,2)$, $(1,2,3,4,2)$, and $(4)$ are subscores of $(1,2,3,4,2)$.

Note that $(1,3)$ is not a subscore.

If two subscores start or end at different positions in the piece, we call them “different subscores”.

If all numbers at any two positions in a subscore are different, we call it a “good subscore”.

The performers are very picky, and they require the following for the score:

1. All notes must be less than $m$.
2. There are $k$ good subscores in the score.

They now ask you whether you can construct such a score.

Input Format

The first line contains three integers $n, m, k$. Their meanings are described in the statement.

Output Format

Output one line with $n$ integers, representing the score required by the performers.

If there are one or more valid scores, output the lexicographically smallest one. If it is impossible to construct a score that satisfies the requirements, output -1.

3 2 5

1 2 1

5 5 14

1 5 3 2 1

5 5 50

-1

Hint

For $20\%$ of the testdata: $1 \le n \le 16$, $m = 2$, $1 \le k \le 1000$.

For another $20\%$ of the testdata: $1 \le n \le 10^6$, $m = 2$, $1 \le k \le 10^{18}$.

For another $25\%$ of the testdata: $1 \le n \le 10^6$, $m = n$, $1 \le k \le 10^{18}$.

For $100\%$ of the testdata: $1 \le n \le 10^6$, $1 \le m \le n$, $1 \le k \le 10^{18}$.

Translated by ChatGPT 5