Problem Description

You are given an integer sequence of length $ N $, $A_1, A_2, \cdots, A_N$. Consider an operation where you select $ K $ elements from this sequence and arrange them into a new sequence while preserving their relative order. However, you can only select both $ A_i $ and $ A_j $ $(i \neq j)$ if $|i - j| \geq D$.

Determine the smallest lexicographical sequence that can be formed under these constraints. If such an operation is impossible, output $ -1 $.

A sequence $x_1, x_2, \cdots, x_K$ is lexicographically smaller than $y_1, y_2, \cdots, y_K$ if the two sequences differ and $ x_i < y_i $ for the smallest integer $ i $ such that $x_i \neq y_i$.

Input Format

The input is given from the standard input in the following format:

$ N $ $ K $ $ D $ $ A_1 $ $ A_2 $ $\cdots$ $ A_N $

Output Format

Output the smallest lexicographical sequence that can be obtained if the operation is possible; otherwise, output $ -1 $.

Sample Input and Output

Sample Input #1

3 2 2
3 1 4

Sample Output #1

3 4

Sample Input #2

3 3 2
3 1 4

Sample Output #2

-1

Sample Input #3

3 2 1
3 1 4

Sample Output #3

1 4

Sample Input #4

4 2 2
3 6 5 5

Sample Output #4

3 5

Notes/Hints

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq D \leq N$
• $1 \leq K \leq N$
• $0 \leq A_i \leq 10^9$
• All inputs are integers

Sample Explanation 1

The sequence $ A $ is $\{3, 1, 4\}$. Under $ D = 2 $, the only way to select $ K = 2 $ elements is to choose the 1st and 3rd elements of $ A $, resulting in $\{3, 4\}$. Therefore, output $\{3, 4\}$.

Sample Explanation 2

The sequence $ A $ is $\{3, 1, 4\}$. Under $ D = 2 $, it is impossible to select $ K = 3 $ elements. Therefore, output $ -1 $.

Sample Explanation 3

The sequence $ A $ is $\{3, 1, 4\}$. Under $ D = 1 $, there are three ways to select $ K = 2 $ elements:
- Choose the 1st and 2nd elements of $ A $, resulting in $\{3, 1\}$.
- Choose the 1st and 3rd elements of $ A $, resulting in $\{3, 4\}$.
- Choose the 2nd and 3rd elements of $ A $, resulting in $\{1, 4\}$.
Therefore, output $\{1, 4\}$.

Sample Explanation 4

The sequence $ A $ is $\{3, 6, 5, 5\}$. Under $ D = 2 $, there are three ways to select $ K = 2 $ elements:
- Choose the 1st and 3rd elements of $ A $, resulting in $\{3, 5\}$.
- Choose the 1st and 4th elements of $ A $, resulting in $\{3, 5\}$.
- Choose the 2nd and 4th elements of $ A $, resulting in $\{6, 5\}$.
Therefore, output $\{3, 5\}$.

见题面 Input 部分

见题面 Output 部分