Nice Array

You're given an array $A$ of length $N$, and an integer $K$. $A$ is said to be a *nice array* if there exists an array $B$ of length $N$ satisfying the following conditions: 1. For every index $i$ ($1 \leq i \leq N$), $B_i = \left\lfloor \frac{A_i}{K} \right\rfloor$, or $B_i = \left\lceil \frac{A_i}{K} \right\rceil$; and 2. $B_1 + B_2 + \ldots + B_N = 0$. Is $A$ a *nice array*? Note that $\left