Problem Description

Note: The notes in the musical score are represented by numbers.

A sub-score is defined as a "non-empty continuous sequence of notes." Specifically, after sorting and removing duplicates from a sequence, the difference between adjacent values is 1.

For example:
$(3,4,2),(1,2,3,4,2),(4)$ are sub-scores of $(1,2,3,4,2)$.

Note that $(1,3)$ is not a sub-score.

If two sub-scores start or end at different positions in the composition, they are considered "different sub-scores."

A sub-score is called "good" if any two numbers at different positions within it are distinct.

The performers are very demanding and have the following requirements for the score:

1. All notes must be less than $m$.
2. There must be exactly $k$ good sub-scores in the sub-scores.

They have come to you to ask if it is possible to fulfill these operations.

Input Format

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

Output Format

One line with $n$ integers, representing the score desired by the performers.

If there is one or more scores that meet the requirements, output the one with the smallest lexicographical order; if it is not possible to form the desired score, output -1.

Sample Input and Output

Sample Input #1

3 2 5

Sample Output #1

1 2 1

Sample Input #2

5 5 14

Sample Output #2

1 5 3 2 1

Sample Input #3

5 5 50

Sample Output #3

-1

Notes

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

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

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

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

见题面 Input 部分

见题面 Output 部分