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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>

using namespace std;

#define rep(i, n) for (int i = 0; i < n; i++)
#define vec vector
#define ll long long

int n, m;
ll k;
vec<int> x;
vec<int> a;
vec<int> keep;

vec<int> mul(ll time, vec<int> go)
{
	if (time == 1) return go;
	vec<int> ret(n - 1);
	go = mul(time / 2, go);
	rep(i, n - 1) {
		ret[i] = go[go[i]];
		if (time % 2) ret[i] = keep[ret[i]];
	}
	return ret;
}
	

int main(void)
{
	cin >> n;
	x.resize(n);
	rep(i, n) cin >> x[i];
	cin >> m >> k;
	a.resize(m);
	rep(i, m) cin >> a[i];
	rep(i, m) a[i]--;

	vec<int> aida(n - 1);
	rep(i, n - 1) {
		aida[i] = x[i + 1] - x[i];
	}

	vec<int> go(n - 1);
	rep(i, n - 1) go[i] = i;
	rep(i, m) {
	   int temp = go[a[i]];
	   go[a[i]] = go[a[i] - 1];
	   go[a[i] - 1] = temp;
	}
	keep = go;
	go = mul(k, go);

	cout << x[0] << endl;
	rep(i, n - 1) {
		x[i + 1] = x[i] + aida[go[i]];
		cout << x[i + 1] << endl;
	}
	return 0;
}