Modular Knapsack

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.

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

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

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

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