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 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>

typedef long long int int64;

void run(void){
  int n;
  scanf("%d",&n);
  int *x=(int *)calloc(n,sizeof(int));
  int i;
  for(i=0;i<n;i++) scanf("%d",x+i);
  int m;
  int64 k;
  scanf("%d%lld",&m,&k);
  int *s=(int *)calloc(n-1,sizeof(int));
  for(i=0;i<n-1;i++) s[i]=i;
  while(m--){
    int a;
    scanf("%d",&a);
    a-=2;
    int swap=s[a];
    s[a]=s[a+1];
    s[a+1]=swap;
  }
  int *t=(int *)calloc(n-1,sizeof(int));
  int *tmp=(int *)calloc(n-1,sizeof(int));
  for(i=0;i<n-1;i++) t[i]=i;
  while(k>0){
    if(k&1){
      for(i=0;i<n-1;i++) tmp[i]=s[t[i]];
      for(i=0;i<n-1;i++) t[i]=tmp[i];
    }
    for(i=0;i<n-1;i++) tmp[i]=s[s[i]];
    for(i=0;i<n-1;i++) s[i]=tmp[i];
    k>>=1;
  }
  int *y=(int *)calloc(n-1,sizeof(int));
  for(i=0;i<n-1;i++) y[i]=x[i+1]-x[i];
  for(i=0;i<n-1;i++) tmp[i]=y[t[i]];
  for(i=0;i<n-1;i++) y[i]=tmp[i];
  int64 ans=x[0];
  printf("%lld\n",ans);
  for(i=1;i<n;i++){
    ans+=y[i-1];
    printf("%lld\n",ans);
  }
}

int main(void){
  run();
  return 0;
}