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;
#define rep(i,a) for(int i=0;i<(a);i++)
const ll MOD=1000000007;

int N,M;
ll X[101010],K;
int A[62][101010], dy[101010];

int main(){
  cin>>N;
  rep(i,N) cin>>X[i];
  rep(i,N-1) A[0][i]=dy[i]=i;
  cin>>M>>K;
  rep(i,M){
    int x; cin>>x; x--;
    swap(A[0][x-1],A[0][x]);
  }
  rep(i,61){
    rep(j,N){
      A[i+1][j]=A[i][A[i][j]];
    }
  }
  
  rep(i,61){
    if(K&(1LL<<i)){
      rep(j,N) dy[j]=A[i][dy[j]];
    }
  }
  ll sum=X[0];
  rep(i,N){
    cout<<sum<<endl;
    sum+=X[dy[i]+1]-X[dy[i]];
  }
  return 0;
}