Solve the problem for when the integers have to be in the range $$$[1, k]$$$ for some $$$k$$$.

Solve the problem for multisets faster than $$$\mathcal{O}(n^3)$$$.

Prove and construct exact bound for the answer.

Solve the problem in $$$\mathcal{O}(nk)$$$.

Write a checker for this problem.

Solve the problem purely with generating functions.