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 <vector>
#include <algorithm>
#include <cstdio>
using namespace std;
 
vector<int> mul(vector<int> &a,vector<int> &b){
	int i=0,n=a.size();
	vector<int> r(n);
	for(i=0;i<n;i++)r[i]=a[b[i]];
	return r;
}
 
int main(){
	int n,m,i,x,s;
	long long k;
	scanf("%d",&n);
	vector<int> t(n),e(n),a(n);
	for(i=0;i<n;i++)scanf("%d",&a[i]),t[i]=i,e[i]=i;
	for(i=n-1;i;i--)a[i]-=a[i-1];
	scanf("%d%lld",&m,&k);
	for(i=0;i<m;i++)scanf("%d",&x),swap(t[x-2],t[x-1]);
	for(;k;k>>=1){
		if(k&1)e=mul(e,t);
		t=mul(t,t);
	}
	for(k=a[i=0];i<n;i++)printf("%lld\n",k),k+=a[e[i]+1];
}