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 lint;
typedef pair<int, int> pi;
 
int n, a[100005];
lint q, k;
int spt[66][100005];
 
int main(){
	cin >> n;
	for(int i=1; i<=n; i++){
		scanf("%d",&a[i]);
		spt[0][i] = i;
	}
	spt[0][n] = 0;
	cin >> q >> k;
	for(int i=0; i<q; i++){
		int x;
		scanf("%d",&x);
		swap(spt[0][x-1], spt[0][x]);
	}
	for(int i=1; i<60; i++){
		for(int j=1; j<n; j++){
			spt[i][j] = spt[i-1][spt[i-1][j]];
		}
	}
	lint cur = a[1];
	printf("%lld\n", cur);
	for(int i=1; i<n; i++){
		int pos = i;
		for(int j=0; j<60; j++){
			if((k >> j) & 1) pos = spt[j][pos];
		}
		cur += a[pos+1] - a[pos];
		printf("%lld\n", cur);
	}
}