No sequence

Alice gave Bob $3$ integers $N, K,$ and $S$. Help Bob find an $S$-good sequence. A sequence $B$ of length $N$ is called $S$-good if the following conditions are met: - $B_i \in \{-1, 0, 1\}$ for each $1 \leq i \leq N$ - $\sum_{i=1}^N B_i\cdot K^{i-1} = S$ If there are multiple $S$-good sequences, print **any** of them. **If no $S$-good sequence exists, print $-2$.** ### Input - The first line