Problem:
Score : 800 points

Problem Statement

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}.

Sample Input 1

3
-1 0 2
1 1
2

Sample Output 1

-1.0
1.0
2.0

Rabbit 2 will perform the jump.
If rabbit 1 is chosen, the coordinate of the destination will be -2.
If rabbit 3 is chosen, the coordinate of the destination will be 4.
Thus, the expected value of the coordinate of the eventual position of rabbit 2 is 0.5×(-2)+0.5×4=1.0.

Sample Input 2

3
1 -1 1
2 2
2 2

Sample Output 2

1.0
-1.0
1.0

x_i may not be distinct.

Sample Input 3

5
0 1 3 6 10
3 10
2 3 4

Sample Output 3

0.0
3.0
7.0
8.0
10.0

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
using System.IO;

class Program
{
    static bool Equals(long[] a, long[] b)
    {
        int N = a.Length;
        for (int i = 0; i < N; ++i) { if (a[i] != b[i]) { return false; } }
        return true;
    }
    static long Count(long[] x, long K, int[] a)
    {
        long[] p1 = (long[])x.Clone();
        for (long i = 1; i <= K; ++i)
        {
            long[] p2 = (long[])p1.Clone();
            foreach (int n in a)
            {
                p2[n - 1] += (p2[n] - p2[n - 1]) + (p2[n - 2] - p2[n - 1]);
            }
            if (Equals(p2, x))
            {
                return i;
            }
            p1 = p2;
        }
        return 1;
    }
    static void Main(string[] args)
    {
        int N = int.Parse(Console.ReadLine());
        long[] x = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        long[] values = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        int M = (int)values[0];
        long K = values[1];
        int[] a = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        long count = Count(x, K, a);
        long[] p1 = (long[])x.Clone();
        for (long i = 0; i < K % count; ++i)
        {
            long[] p2 = (long[])p1.Clone();
            foreach (int n in a)
            {
                p2[n - 1] += (p2[n] - p2[n - 1]) + (p2[n - 2] - p2[n - 1]);
            }
            p1 = p2;
        }
        foreach (long n in p1) { Console.WriteLine(n); }
    }
}