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: Accepted)

using System;
using System.Text;
using System.Collections.Generic;
class Solve{
    int N;
    long[] x;
    int M;
    long K;
    int[] a;
    int[] original;
    public Solve(){}
    public static int Main(){
        new Solve().Calc();
        return 0;
    }
    void Calc(){
        getinput();
        int[] swap;
        long[] dx = new long[N-1];
        long[] adx = new long[N-1];
        original = new int[N-1];
        for(int i=0;i<N-1;i++){
            original[i] = i;
        }
        for(int i=0;i<M;i++){
            int j = original[a[i]-1];
            original[a[i]-1] = original[a[i]];
            original[a[i]] = j;
        }
        swap = m(K);
        for(int i=0;i<N-1;i++){
            dx[i] = x[i+1]-x[i];
        }
        for(int i=0;i<N-1;i++){
            adx[i] = dx[swap[i]]; 
        }
        StringBuilder sb = new StringBuilder();
        long count = x[0];
        sb.Append(count+"\n");
        for(int i=0;i<N-1;i++){
            count += adx[i];
            sb.Append(count+"\n");
        }
        Console.Write(sb.ToString());
    }
    int[] m(long k){
        if(k <= 1){
            return original;
        }
        else if(k%2 == 0){
            int[] s = m(k/2);
            int[] t = new int[N-1];
            for(int i=0;i<N-1;i++){
                t[i] = s[s[i]];
            }
            return t;
        }
        else{
            int[] s = m(k-1);
            int[] t = new int[N-1];
            for(int i=0;i<N-1;i++){
                t[i] =original[s[i]];
            }
            return t;
        }
    }
    void getinput(){
        N = int.Parse(Console.ReadLine());
        x = new long[N];
        string[] str = Console.ReadLine().Split(' ');
        for(int i=0;i<N;i++){
            x[i] = Int64.Parse(str[i]);
        }
        str = Console.ReadLine().Split(' ');
        M = int.Parse(str[0]);
        K = Int64.Parse(str[1]);
        a = new int[M];
        str = Console.ReadLine().Split(' ');
        for(int i=0;i<M;i++){
            a[i] = int.Parse(str[i])-1;
        }
    }    
}