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 <bits/stdc++.h>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

int n;
int x[200000],y[200000];

vector<int>merge(vector<int>&a,vector<int>&b){
	vector<int>res(n);
	rep(i,n){
		res[i]=a[b[i]];
	}
	return res;
}
int main(){
	scanf("%d",&n);
	rep(i,n){
		scanf("%d",&x[i]);
		y[i]=x[i];
		if(i)y[i]-=x[i-1];
	}
	int m;ll K;cin>>m>>K;
	vector<int>v(n);
	rep(i,n)v[i]=i;
	rep(i,m){
		int d;scanf("%d",&d);d--;
		swap(v[d],v[d+1]);
	}
	vector<int>ans(n);
	rep(i,n)ans[i]=i;
	while(K){
		if(K&1){
			ans=merge(ans,v);
		}
		v=merge(v,v);
		K>>=1;
	}
	ll sum=0;
	rep(i,n){
		sum+=y[ans[i]];
		printf("%lld\n",sum);
	}
}