23642번 - Modular Knapsack 다국어

문제

Today you should solve unusual knapsack problem. You are given $n$ items, $i$-th of them has weight $w_i$ and cost $c_i$. Also a prime $p$ is given. For every remainder $r$ modulo $p$ you should find the maximum total cost of a set of items with total weight having remainder $r$ modulo $p$. All weights and costs in each test except samples are chosen randomly and independently from range $[0 \dots 10^9]$. $n$ and $p$ are chosen manually.

입력

The first line contains two integers $n,ドル $p$ (1ドル\leq n\leq 10^6, 2\leq p\leq 3000$) -- the number of items and the prime modulo.

The next line contains $n$ integers $w_i$ (0ドル\leq w_i\leq 10^9$) --- the weights of items.

The next line contains $n$ integers $c_i$ (0ドル\leq c_i\leq 10^9$) --- the costs of items.

출력

Output one line with $p$ integers. $i$-th of them (0ドル$-indexed) should be equal to the maximum total cost of a set of items with total weight having remainder $i$ modulo $p,ドル or $-1$ if such set doesn't exist.

제한

힌트