Base or Bias

Reyaan has given you the following problem to solve: You are given an integer $K$ in base $B$, represented by an array $A$ of length $N$ such that - $0 \leq A_i \lt B$ for every $1 \leq i \leq N$ - $\sum_{i=1}^N A_i \cdot B^{N-i} = K$ Note that $N \leq B$ in this problem. Find the smallest **non-negative** integer $X$ such that $X+K$ contains *every* digit from $0$ to $B-1$ in its base-$B$ repr