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 PYTHON):

Solution:
ii=lambda:map(int,raw_input().split())
n=int(raw_input())
x=ii()
m,k=ii()
a=ii()
y=[x[i+1]-x[i] for i in range(n-1)]
a=[a[i]-2 for i in range(m)]
p=[i for i in range(n-1)]
for i in a:
    p[i],p[i+1]=p[i+1],p[i]
bit=list(reversed(map(int,list(bin(k)[2:]))))
q=[[] for i in range(len(bit))]
ans=[i for i in range(n)]
for i in range(len(bit)):
    if i==0: q[0]=[p[j] for j in range(n-1)]
    else: q[i]=[q[i-1][q[i-1][j]] for j in range(n-1)]
    if bit[i]:ans=[q[i][ans[j]] for j in range(n-1)]
w=x[0]
print w
for i in range(n-1):
    w+=y[ans[i]]
    print w