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>
#define Rint register int
using namespace std;
typedef long long LL;
const int N = 100003;
int n, m, c[N], d[N], cnt;
LL ans[N], x[N], k;
bool vis[N];
int main(){
	scanf("%d", &n);
	for(Rint i = 1;i <= n;i ++) scanf("%lld", x + i), c[i] = i;
	for(Rint i = n;i;i --) x[i] -= x[i - 1];
	scanf("%d%lld", &m, &k);
	for(Rint i = 1;i <= m;i ++){
		int v; scanf("%d", &v); swap(c[v], c[v + 1]);
	}
	for(Rint i = 1;i <= n;i ++) if(!vis[i]){
		cnt = 0;
		for(Rint j = i;!vis[j];j = c[j]) vis[d[cnt ++] = j] = true;
		for(Rint j = 0;j < cnt;j ++)
			ans[d[j]] = x[d[(j + k) % cnt]];
	}
	for(Rint i = 1;i <= n;i ++){
		ans[i] += ans[i - 1];
		printf("%lld.0\n", ans[i]);
	}
}