CF722C.Destroying Array

普及/提高-

通过率：0%

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题目描述

You are given an array consisting of $n$ non-negative integers $a_{1},a_{2},...,a_{n}$ .

You are going to destroy integers in the array one by one. Thus, you are given the permutation of integers from $1$ to $n$ defining the order elements of the array are destroyed.

After each element is destroyed you have to find out the segment of the array, such that it contains no destroyed elements and the sum of its elements is maximum possible. The sum of elements in the empty segment is considered to be $0$ .

输入格式

The first line of the input contains a single integer $n$ ( $1<=n<=100000$ ) — the length of the array.

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=10^{9}$ ).

The third line contains a permutation of integers from $1$ to $n$ — the order used to destroy elements.

输出格式

Print $n$ lines. The $i$ -th line should contain a single integer — the maximum possible sum of elements on the segment containing no destroyed elements, after first $i$ operations are performed.

输入输出样例

输入#1
```
4
1 3 2 5
3 4 1 2
```
输出#1
```
5
4
3
0
```
输入#2
```
5
1 2 3 4 5
4 2 3 5 1
```
输出#2
```
6
5
5
1
0
```

输入#3

8
5 5 4 4 6 6 5 5
5 2 8 7 1 3 4 6

输出#3

说明/提示

Consider the first sample:

Third element is destroyed. Array is now $1 3 * 5$ . Segment with maximum sum $5$ consists of one integer $5$ .
Fourth element is destroyed. Array is now $1 3 * *$ . Segment with maximum sum $4$ consists of two integers $1 3$ .
First element is destroyed. Array is now $* 3 * *$ . Segment with maximum sum $3$ consists of one integer $3$ .
Last element is destroyed. At this moment there are no valid nonempty segments left in this array, so the answer is equal to $0$ .

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