Hello, I am preparing a mashup contest, I want to assign scores for each problem. Like a normal codeforces div.

How can I achieve this?

hello codeforces!

Today I thought of this variation of the knapsack problem and I couldn't find a solution.

We have $$$n$$$ items ($$$n$$$ is up to $$$10^{6}$$$). There are $$$sz_i$$$ copies of the $$$i_{th}$$$ item.

$$$\sum sz_i$$$ won't exceed $$$10^6$$$

We can pick more than one copy of each item, if we decided to pick $$$j$$$ copies of the $$$i_{th}$$$ item our score increases by $$$value[i][j]$$$

Our goal is to pick $$$k$$$ ($$$k$$$ is up to $$$10^6$$$) copies in total in a way that will maximize our score.

This sounds very standard to me, what is the solution for that?