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<iostream>
using namespace std;
int n,m;long k;
int x[1<<17],d[1<<17];
int t[1<<17],s[1<<17],b[1<<17];
int main()
{
	cin>>n;
	for(int i=0;i<n;i++)
	{
		cin>>x[i];
		if(i)d[i-1]=x[i]-x[i-1];
	}
	for(int i=0;i<n-1;i++)s[i]=t[i]=i;
	cin>>m>>k;
	for(int i=0;i<m;i++)
	{
		int a;cin>>a;
		t[a-2]^=t[a-1]^=t[a-2]^=t[a-1];
	}
	while(k)
	{
		if(k&1)
		{
			for(int i=0;i<n-1;i++)s[i]=t[s[i]];
		}
		for(int i=0;i<n-1;i++)b[i]=t[t[i]];
		for(int i=0;i<n-1;i++)t[i]=b[i];
		k>>=1;
	}
	long now=x[0];
	cout<<now<<endl;
	for(int i=0;i<n-1;i++)
	{
		now+=d[s[i]];
		cout<<now<<endl;
	}
}