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 PYTHON3):

Solution:
n = int(input())
x = list(map(int, input().split()))
g = [x[i+1]-x[i] for i in range(n-1)]
m, k = map(int, input().split())
A = list(map(int, input().split()))
t = list(range(n-1))
for a in A:
	t[a-2], t[a-1] = t[a-1], t[a-2]
s = list(range(n-1))
while k > 0:
	if k&1:
		s = [s[t[i]] for i in range(n-1)]
	t = [t[t[i]] for i in range(n-1)]
	k >>= 1
new_g = [g[s[i]] for i in range(n-1)]
ans = [x[0]]
for i in range(n-1):
	ans.append(ans[-1] + new_g[i])
print(*ans, sep="\n")