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 JAVA):

Solution:
import java.io.PrintWriter;
import java.util.*;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int N = sc.nextInt();
		int[] x = new int[N];
		for(int i=0; i<N; i++)
			x[i] = sc.nextInt();
		int M = sc.nextInt();
		long K = sc.nextLong();
		int[] a = new int[M];
		for(int i=0; i<M; i++)
			a[i] = sc.nextInt()-1;
		
		int[] map = new int[N-1];
		for(int i=0; i<N-1; i++)
			map[i] = i;
		
		for(int i=0; i<M; i++) {
			int temp = map[a[i]-1];
			map[a[i]-1] = map[a[i]];
			map[a[i]] = temp;
		}
		
		int[] mapK = pow(map, K);
		
		long cur = x[0];
		for(int i=0; i<N; i++) {
			pw.println(cur);
			if(i<N-1)
				cur += x[mapK[i]+1]-x[mapK[i]];
		}
		
		sc.close();
		pw.close();
	}
	
	static int[] pow(int[] m, long K) {
		int[] ans = new int[m.length];
		for(int i=0; i<ans.length; i++)
			ans[i] = i;
		
		while(K>0) {
			if((K&1)!=0) {
				ans = mul(ans, m);
			}
			m = mul(m, m);
			
			K>>=1;
		}
		
		return ans;
	}
	
	static int[] mul(int[] a, int[] b) {
		int[] ans = new int[a.length];
		for(int i=0; i<ans.length; i++)
			ans[i] = a[b[i]];
		return ans;
	}
}