https://usaco.guide/solutions/cses-1665
I think the 3rd bullet point in the solution has an error. It is “j⋅dp[i−1][j+1][k−s]” while I think it should be j + 1 times that dp state (As you have j + 1 choices). My solution which used j + 1 worked but feel free to correct me if I am wrong.