Easy Constructive Problem

For an array $A$ of length $N$ and a non-negative integer $m$, we define the function $f_m(A)$ as $$ f_m(A) = \sum_{i=1}^N A_i \cdot i^m $$ You are given two integers $N$ and $C$. A sequence $A$ of non-negative integers of length $K$ is said to be *good* if it satisfies the following four conditions: 1. $1 \leq K \leq N$ 2. $0 \le A_1 \leq A_2\leq A_3 \leq \ldots \leq A_K$ 3. $f_0(A) = N$ 4. $