Problem: There are N rabbits on a number line. The rabbits are conveniently numbered 1 through N. The coordinate of the initial position of rabbit i is x_i.

The rabbits will now take exercise on the number line, by performing sets described below. A set consists of M jumps. The j-th jump of a set is performed by rabbit a_j (2≤a_j≤N-1). For this jump, either rabbit a_j-1 or rabbit a_j+1 is chosen with equal probability (let the chosen rabbit be rabbit x), then rabbit a_j will jump to the symmetric point of its current position with respect to rabbit x.

The rabbits will perform K sets in succession. For each rabbit, find the expected value of the coordinate of its eventual position after K sets are performed.

Constraints

* 3≤N≤10^5
* x_i is an integer.
* |x_i|≤10^9
* 1≤M≤10^5
* 2≤a_j≤N-1
* 1≤K≤10^{18}

Input

The input is given from Standard Input in the following format:


N
x_1 x_2 ... x_N
M K
a_1 a_2 ... a_M


Output

Print N lines. The i-th line should contain the expected value of the coordinate of the eventual position of rabbit i after K sets are performed. The output is considered correct if the absolute or relative error is at most 10^{-9}.

Examples

Input

3
-1 0 2
1 1
2


Output

-1.0
1.0
2.0


Input

3
1 -1 1
2 2
2 2


Output

1.0
-1.0
1.0


Input

5
0 1 3 6 10
3 10
2 3 4


Output

0.0
3.0
7.0
8.0
10.0

Solution (in CPP):

Solution:
#include<cstdio>
const int MaxN=100010;
int N,x[MaxN],M,p[MaxN],q[MaxN];
long long ans[MaxN],K;
void swp(int&a,int&b){int t=a;a=b;b=t;}
bool vis[MaxN];
int list[MaxN];
int main(){
	scanf("%d",&N);
	for(int i=1;i<=N;i++)scanf("%d",x+i),p[i]=i;
	scanf("%d%lld",&M,&K);
	while(M--){
		int a;scanf("%d",&a);
		swp(p[a-1],p[a]);
	}
	for(int i=0;i<=N;i++)if(!vis[i]){
		int len=0,j=i;
		for(;!vis[j];vis[j]=1,j=p[j])list[len++]=j;
		int r=K%len;
		for(int t=0;t<len;t++)
			p[list[t]]=list[r],r=(r+1)%len;
	}
	for(int i=0;i<=N;i++)q[p[i]]=i;
	for(int i=1;i<=N;i++)ans[q[i-1]]+=x[i],ans[q[i]]-=x[i];
	for(int i=0;i<N;i++)printf("%lld.0\n",ans[i]),ans[i+1]+=ans[i];
}