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:
def process(x, a, k):
    n = len(x)
    f = range(0, n)
    for i in a:
        f[i], f[i+1] = f[i+1], f[i]
    #print 'f=%s' % str(f)
    b = 1
    while b<=k:
        if (k&b)!=0:
            t = [0 for i in xrange(n)]
            for i in xrange(n):
                t[i] = x[f[i]]
            x = [i for i in t]
            #print 'x=%s' % str(x)
        t = [0 for i in f]
        for i in xrange(n):
            t[i] = f[f[i]]
        f = [i for i in t]
        #print 'f=%s' % str(f)
        b <<= 1
    return x

def main():
    n = int(raw_input().strip())
    x = [int(i) for i in raw_input().strip().split()]
    for i in xrange(len(x)-1, 0, -1):
        x[i] = x[i]-x[i-1]
    m, k = [int(i) for i in raw_input().strip().split()]
    a = [int(i) for i in raw_input().strip().split()]
    for i in xrange(len(a)):
        a[i] -= 2
    r = process(x[1:], a, k)
    print x[0]
    for i in xrange(1, len(x)):
        x[i] = x[i-1]+r[i-1]
        print x[i]

if __name__ == '__main__':
    main()