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>
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
#define fo(i,a,b) for(i=a;i<=b;i++)
using namespace std;
typedef long long ll;
const int maxn=1e5+7;
ll i,j,l,k,t,n,m,ans,an[maxn];
ll a[maxn],b[maxn],c[maxn],x,d[maxn],e[maxn];
void gao(ll *x,ll *y){
    ll i;
    fo(i,1,n)d[i]=x[y[i]];
    fo(i,1,n)x[i]=d[i];
}
int main(){
//	freopen("fan.in","r",stdin);
    scanf("%lld",&n);
    fo(i,1,n)scanf("%lld",&a[i]),a[i]=a[i]-x,x=a[i]+x,b[i]=c[i]=e[i]=i;
    scanf("%lld%lld",&m,&k);
    fo(i,1,m)scanf("%lld",&l),swap(b[l],b[l+1]);
    for(;k;k/=2,gao(b,b)){
    	if(k&1)gao(e,b);
	}
	x=0;fo(i,1,n)x+=a[e[i]],printf("%lld.0\n",x);
}