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:
import sys
readline = sys.stdin.readline

def merge(A, B):
    N = len(A)
    res = [B[A[i]] for i in range(N)]
    return res

N = int(readline())

X = list(map(int, readline().split()))
M, K = map(int, readline().split())
A = list(map(lambda x:int(x)-1, readline().split()))
Y = [x2 - x1 for x1, x2 in zip(X, X[1:])]

 
P = list(range(N))
for a in A:
    P[a], P[a+1] = P[a+1], P[a]
stack = [P]
for _ in range(65):
    stack.append(merge(stack[-1], stack[-1]))

E = list(range(N))
for i in range(K.bit_length()):
    if (1<<i) & K:
        E = merge(E, stack[i])

Ans = [0]*N
Ans[0] = X[0]
for i in range(1, N):
    Ans[i] = Ans[i-1] + Y[E[i]-1]
print('\n'.join(map(str, Ans)))