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 N 100009
using namespace std;

int n,m,a[N],b[N],p[N],q[N],np[N]; long long tot;
int main(){
	scanf("%d",&n);
	int i; long long now; 
	for (i=1; i<=n; i++) scanf("%d",&a[i]);
	scanf("%d%lld",&m,&tot);
	for (i=1; i<=m; i++) scanf("%d",&b[i]);
	for (i=1; i<n; i++) p[i]=i;
	for (i=1; i<=m; i++) swap(p[b[i]-1],p[b[i]]);
	for (i=1; i<n; i++) q[i]=i;
	for (; tot; tot>>=1){
		if (tot&1){
			for (i=1; i<n; i++) np[i]=q[p[i]];
			for (i=1; i<n; i++) q[i]=np[i];
		}
		for (i=1; i<n; i++) np[i]=p[p[i]];
		for (i=1; i<n; i++) p[i]=np[i];
	}
	for (i=n; i>1; i--) a[i]-=a[i-1];
	for (i=1,now=a[1]; i<=n; now+=a[q[i]+1],i++)
		printf("%lld\n",now);
	return 0;
}