How can the following summation be written in terms of $N$?

Question

Suppose that $N=\sum_{j=1}^{Q}k_j,$ where the $0\leq k_j$ are integers. Then, what is $\sum_{j=1}^{Q}jk_j$ in terms of $N$ and possibly $Q$. Meaning, if $$f=\sum_{j=1}^{Q}jk_j,$$ what is either $f(N)$ or $f(N, Q)$? I have made several attempts at this problem including finding elementary upper and lower bounds, such as $f(N)=N$. But, I am hoping to find a more suitable answer, even if it is an upper or lower bound that improves on mine. I have also tried considering $f(N)=cN$ where $c$ is some constant and $f(N)=cN^{c_0}$ where both $c$ and $c_0$ are constant, each to no avail. I do not know how else to continue. (I understand that considering $$c=\frac{\sum_{j=1}^{Q}jk_j}{\sum_{j=1}^{Q}k_j}$$ for the first case is reminiscent of a center of mass problem. )