Andi is a mathematician, a computer scientist, and a songwriter. After spending so much time writing songs, he finally writes a catchy melody that he thought as his best creation. However, the singer who will sing the song/melody has a unique vocal range, thus, an adjustment may be needed.

A melody is defined as a sequence of $$$N$$$ notes which are represented by integers. Let $$$A$$$ be the original melody written by Andi. Andi needs to adjust $$$A$$$ into a new melody $$$B$$$ such that for every $$$i$$$ where $$$1 \le i < N$$$:

• If $$$A_i < A_{i+1}$$$, then $$$B_i < B_{i+1}$$$.
• If $$$A_i = A_{i+1}$$$, then $$$B_i = B_{i+1}$$$.
• If $$$A_i > A_{i+1}$$$, then $$$B_i > B_{i+1}$$$.
• $$$|B_i - B_{i+1}| \le K$$$, i.e. the difference between two successive notes is no larger than $$$K$$$.

Help Andi to determine whether such $$$B$$$ exists, and find the lexicographically smallest $$$B$$$ if it exists. A melody $$$X$$$ is lexicographically smaller than melody $$$Y$$$ if and only if there exists $$$j$$$ ($$$1 \le j \le N$$$) such that $$$X_i = Y_i$$$ for all $$$i < j$$$ and $$$X_{j} < Y_{j}$$$.

For example, consider a melody $$$A = \{1,3,5,6,7,8,9,10,3,7,8,9,10,11,12,12\}$$$ as shown in the following figure. The diagonal arrow up in the figure implies that $$$A_i < A_{i+1}$$$, the straight right arrow implies that $$$A_i = A_{i+1}$$$, and the diagonal arrow down implies that $$$A_i > A_{i+1}$$$.

Supposed we want to make a new melody with $$$L = 1$$$, $$$R = 8$$$, and $$$K = 6$$$. The new melody $$$B = \{1,2,3,4,5,6,7,8,2,3,4,5,6,7,8,8\}$$$ as shown in the figure satisfies all the requirements, and it is the lexicographically smallest possible.