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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AGC006_C
{
    class Program
    {
        static long N, M, K;
        static double[] ans;
        static long MAX = 20;
        static StringBuilder sb = new StringBuilder();
        static void Main(string[] args)
        {

            N = scan[0];
            ans = new double[N];

            var g = scan;
            var x = new double[N];
            for (long i = 0; i < N; i++)
            {
                x[i] = g[i];
            }
            var t = scan;
            M = t[0]; K = t[1];
            MAX = Math.Min(MAX, K);

            var a = scan;
            var c = new double[N];
            for (long i = 0; i < N; i++)
            {
                c[i] = x[i];
            }
            back(c, a, 0, 0.5, 1);
            go(x, a, 0, 0.5, 1);

            var d = new double[N];

            for (long i = 1; i < MAX; i++)
            {
                
                for (long j = 0; j < N; j++)
                {
                    c[j] = ans[j];
                    d[j] = ans[j];
                }
                ans = new double[N];
                back(c, a, 0, 0.5, 1);
                go(d, a, 0, 0.5, 1);
            }

            for (long i = 0; i < N; i++)
            {
                sb.AppendLine(ans[i].ToString("F9"));
            }
            Console.Write(sb);
        }
        static void back(double[] X, long[] A, long cnt, double per, long d)
        {
            
            if (cnt == M)
            {
                per += per;
                for (long i = 0; i < N; i++)
                {    
                    ans[i] += per * X[i];
                }
                return;
            }
            var C = new double[N];
           
            per /= 2;
            X[A[cnt] - 1] = X[A[cnt] - 2] * 2 - X[A[cnt] - 1];
            for (long i = 0; i < N; i++)
            {
                C[i] = X[i];
            }
            //Console.WriteLine(X[A[cnt] - 1]);
            back(C, A, cnt + 1, per, d);
            go(X, A, cnt + 1, per, d);

        }
        static void go(double[] X, long[] A, long cnt, double per,long d)
        {

            if (cnt == M)
            {
                return;
            }

            var C = new double[N];
           
            per /= 2;

            X[A[cnt] - 1] = X[A[cnt]] * 2 - X[A[cnt] - 1];
            for (long i = 0; i < N; i++)
            {
                C[i] = X[i];
            }
            //Console.WriteLine(X[A[cnt] - 1]);
            back(C, A, cnt + 1, per, d);
            go(X, A, cnt + 1, per, d);
        }
        static long[] scan { get { return Array.ConvertAll(Console.ReadLine().Split(), long.Parse); } }
    }
}