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:
from math import log

n = int(raw_input())
x = map(int, raw_input().split())
m, k = map(int, raw_input().split())
a = map(lambda x:int(x) - 2, raw_input().split())

logk = log(k, 2)
dy = [x[i + 1] - x[i] for i in xrange(n - 1)]
swap = [range(n - 1) for _ in xrange(int(logk + 1))]

for i in xrange(m):
    swap[0][a[i]], swap[0][a[i] + 1] = swap[0][a[i] + 1], swap[0][a[i]]

j = 1
while j <= logk:
    for i in xrange(n - 1):
        swap[j][i] = swap[j - 1][swap[j - 1][i]]
    j += 1

last = range(n - 1)
j = 0
while k >> j > 0:
    if (k >> j) & 1 == 1:
        for i in xrange(n - 1):
            last[i] = swap[j][last[i]]
    j += 1

ans = x[0]
print(ans)
for i in xrange(n - 1):
    ans += dy[last[i]]
    print(ans)