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>
using namespace std;

typedef long long  LL;
LL n,m,k,x[100010],a[100010],_[100010];

void mul(LL *a,LL *b)
{
	for (int i=1; i<=n; i++)  _[i]=a[b[i]];
	for (int i=1; i<=n; i++)  a[i]=_[i];
}

void work()
{
	scanf("%lld",&n);
	for (int i=1; i<=n; i++)  scanf("%lld",&x[i]),a[i]=i;
	for (int i=n; i; i--)  x[i]-=x[i-1];
	scanf("%lld %lld",&m,&k);
	for (int i=1,x; i<=m; i++)  scanf("%d",&x),swap(a[x],a[x+1]);
	while (k)
		{
			if (k&1)  mul(x,a);
			mul(a,a),k>>=1;
		}
	for (int i=1; i<=n; i++)  x[i]+=x[i-1],printf("%lld\n",x[i]);
}

int main()
{
	work();
	return 0;
}