프로그래밍의 벗 PivotOJ

문제

Dragonflies can be seen around ponds at Botanic Gardens and Bishan Park. In one of the denser forested areas, Benson the Rabbit has noted down $n$ ponds that the dragonflies fly around. At pond $i$ ( $1 ≤ i ≤ n$ ), there are $b [i]$ bugs that the dragonflies can eat. The bugs at pond $i$ belong to species $s [i]$ .

Benson has also noted down $n - 1$ trails. Each trail $j$ ( $1 ≤ j < n$ ) connects 2 distinct ponds $u [j]$ and $v [j]$ bidirectionally. Dragonflies can travel from any pond to any other pond using only the trails.

Benson has captured $d$ dragonflies and intends to release them one at a time at pond $1$ . Dragonfly $k$ ( $1 ≤ k ≤ d$ ) has a home pond of $h[k] \ne 1$ and will travel to pond $h [k]$ without visiting any pond more than once using only the trails. These dragonflies will be released in increasing order from dragonfly $1$ to dragonfly $d$ . After a dragonfly is released, it will eat a single bug (if there is one or more bugs remaining) at every pond that it visits (including pond $1$ ), reducing the number of bugs at each of those ponds by $1$ if it is not $0$ .

Help Benson determine the number of distinct species of bugs eaten during the journey of each of the $d$ dragonflies.

입력

The input format is as follows:

The first line of input contains $2$ spaced integers $n$ and $d$ respectively.
The next line of input contains $n$ spaced integers $b[1], b[2], \cdots , b[n]$ .
The next line of input contains $n$ spaced integers $s[1], s[2], \cdots , s[n]$ .
The next line of input contains $d$ spaced integers $h[1], h[2], \cdots , h[d]$ .
The next $n - 1$ lines of input contains $2$ spaced integers each. The $i$ ^th of these lines contains $u [i]$ and $v [i]$ respectively.

출력

Output a single line with $d$ spaced integers. The $k$ ^th of these integers should be the number of distinct species of bugs eaten by the $k$ ^th dragonfly.

Dragonfly

문제

입력

출력

예제

예제 1

예제 2