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()))
m,k = map(int,input().split())
a = list(map(int,input().split()))
b = []
x2 = []
c = []
for i in range(1,n):
  b.append(i-1)
  x2.append(x[i]-x[i-1])
for i in range(m):
  to = a[i]-1
  b[to],b[to-1] = b[to-1],b[to]
c = [-1] * (n-1)
for i in range(n-1):
  c[b[i]] = i
for i in range(60):
  x3 = [0]*(n-1)
  if k&(1<<i):
    for i in range(n-1):
      x3[c[i]] = x2[i]
    x2 = x3
  c2 = [-1] * (n-1)
  for i in range(n-1):
    c2[i] = c[c[i]] 
  c = c2
s = x[0]
print(s)
for i in x2:
  s += i
  print(s)