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;

#define int long long

signed main(){
  int n;cin>>n;
  vector<int> v(n);
  for(int i=0;i<n;i++)cin>>v[i];
  for(int i=n-1;i;i--)v[i]-=v[i-1];
  int m,k;cin>>m>>k;
  vector<int> a(m);
  for(int &p:a){cin>>p;p--;}
  vector<int> b(n);
  for(int i=0;i<n;i++)b[i]=i;
  for(int i=0;i<m;i++)swap(b[a[i]],b[a[i]+1]);
  while(k){
    if(k&1){
      vector<int>tmp(n);
      for(int i=0;i<n;i++)tmp[i]=v[b[i]];
      for(int i=0;i<n;i++)v[i]=tmp[i];
    }
    k>>=1;
    vector<int> tmp(n);
    for(int i=0;i<n;i++)tmp[i]=b[b[i]];
    for(int i=0;i<n;i++)b[i]=tmp[i];
  }
  cout<<v[0]<<endl;
  for(int i=1;i<n;i++){
    v[i]+=v[i-1];
    cout<<v[i]<<endl;
  }
}