Problems
Hexodoku
Hexodoku
Sudoku is an amazing game. Many people have fun solving it. They say that a legendary programmer had spent just \textbf{7} minutes on writing a program that solves standard sudoku. That's über cool, don't you think? And now he has solved another problem. Can you do the same?
Consider a non-standard hexagonal Sudoku board:
\includegraphics{https://static.e-olymp.com/content/7e/7e0c79e1baf96d1777ff8d0166af7149bb688c6b.jpg}
The cells are numbered from \textbf{1} to \textbf{31}.
According to the rules, numbers (from \textbf{1} to \textbf{K}) can be placed in the cells with the condition that all numbers in the same row (rows are located in three directions) must be different.
\includegraphics{https://static.e-olymp.com/content/46/469a2f8ee96401bfb8e08ee9340b1920a4aee20a.jpg}
Additionally, for each of the marked cells, the number in marked cell and all numbers in adjacent cells must also differ from each other.
\includegraphics{https://static.e-olymp.com/content/41/412e5cda43a232266638b2562afb540857322f8b.jpg}
Must be different
\includegraphics{https://static.e-olymp.com/content/7f/7fb0fdd59be97abf9fb42682826638b84d874ede.jpg}
Some numbers may already be placed in the cells according to the rules. You are to find \textbf{N}^\{-th\} solution in lexicographical order, if it exists.
Let \textbf{A_i} be the number in the cell \textbf{i} in solution \textbf{A}, and \textbf{B_i} --- the number in the cell \textbf{i} in solution \textbf{B}. Solution \textbf{A} is lexicographically smaller than solution \textbf{B}, if such \textbf{j} exists that for each \textbf{i} where \textbf{i} < \textbf{j}: \textbf{A_i = B_i} and \textbf{A_j} < \textbf{B_j}.
\InputFile
First line of input contains two integers \textbf{K} and \textbf{N}.
\begin{itemize}
\item \textbf{7} ≤ \textbf{K} ≤ \textbf{31}
\item \textbf{1} ≤ \textbf{N} ≤ \textbf{100000}
\end{itemize}
Second line contains \textbf{31} integer numbers: \textbf{A_i} (\textbf{1} ≤ \textbf{i} ≤ \textbf{31}) is the number standing in the cell \textbf{i}.
\begin{itemize}
\item \textbf{1} ≤ \textbf{A_i} ≤ \textbf{K}, or \textbf{0}, if there is no number in this cell.
\end{itemize}
\OutputFile
First line of output should contain an answer:
\begin{itemize}
\item "\textbf{Found}" --- if the solution has been found.
\item "\textbf{No way}" --- if there is no N-th solution.
\end{itemize}
If the solution has been found, the second line of output should contain the \textbf{N}^\{-th\} solution in the same format as in input.
This is the first example above:
\includegraphics{https://static.e-olymp.com/content/33/33c305074d68cdfe135bf6ddd0adb2290d71e88e.jpg}
Input example #1
8 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Output example #1
Found 1 2 1 3 4 5 2 2 4 6 7 1 3 7 5 1 8 6 2 1 3 4 5 7 8 6 7 2 3 5 8