722C - Destroying Array 线段树

Destroying Array

output

standard output

You are given an array consisting of n non-negative integersa₁, a₂, ..., a_n.

You are going to destroy integers in the array one by one. Thus, you are given the permutation of integers from1 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 be0.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the length of the array.

The second line contains n integers a₁, a₂, ..., a_n (0 ≤ a_i ≤ 10⁹).

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

Output

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 firsti operations are performed.

Examples

Input

41 3 2 53 4 1 2

Output

5430

Input

51 2 3 4 54 2 3 5 1

Output

65510

Input

85 5 4 4 6 6 5 55 2 8 7 1 3 4 6

Output

18161188660

Note

Consider the first sample:

1. Third element is destroyed. Array is now 1 3  *  5. Segment with maximum sum5 consists of one integer 5.
2. Fourth element is destroyed. Array is now 1 3  *   * . Segment with maximum sum4 consists of two integers 1 3.
3. First element is destroyed. Array is now  *  3  *   * . Segment with maximum sum3 consists of one integer 3.
4. Last element is destroyed. At this moment there are no valid nonempty segments left in this array, so the answer is equal to0. 

使用线段树求出区间和并维护

#include<stdio.h>#include<algorithm>#include<string.h>using namespace std;const int maxm=100005;typedef struct{int l,r,ll,rr;__int64 ls,rs,ms;}H;H tree[maxm*4];__int64 f[maxm*4];void make(int a,int b,int num);void push_back(int num,int len);void update(int k,int num);int main(){int n,i,j,k,sum,m;scanf("%d",&n);for(i=1;i<=n;i++)scanf("%I64d",&f[i]);make(1,n,1);for(i=1;i<=n;i++){scanf("%d",&k);update(k,1);printf("%I64d\n",tree[1].ms);}return 0;}void make(int a,int b,int num){tree[num].ll=tree[num].rr=b-a+1;tree[num].l=a;tree[num].r=b;if(a==b){tree[num].ls=tree[num].rs=tree[num].ms=f[a];return;}int mid=(a+b)/2;make(a,mid,num*2);make(mid+1,b,num*2+1);tree[num].ls=tree[num].rs=tree[num].ms=tree[num*2].ms+tree[num*2+1].ms;}void update(int k,int num){int s=tree[num].l,e=tree[num].r;if(s==e){tree[num].ll=tree[num].rr=0;tree[num].ls=tree[num].rs=tree[num].ms=0;return;}int mid=(s+e)/2;if(k<=mid)update(k,num*2);else if(k>mid)update(k,num*2+1);push_back(num,e-s+1);}void push_back(int num,int len){tree[num].ls=tree[num*2].ls;tree[num].ll=tree[num*2].ll;if(tree[num].ll==len-len/2){tree[num].ll+=tree[num*2+1].ll;tree[num].ls+=tree[num*2+1].ls;}tree[num].rs=tree[num*2+1].rs;tree[num].rr=tree[num*2+1].rr;if(tree[num].rr==len/2){tree[num].rr+=tree[num*2].rr;tree[num].rs+=tree[num*2].rs;}tree[num].ms=max(tree[num*2].ms,tree[num*2+1].ms);tree[num].ms=max(tree[num].ms,tree[num*2].rs+tree[num*2+1].ls);}