Problem: 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}.

Examples

Input

3
-1 0 2
1 1
2


Output

-1.0
1.0
2.0


Input

3
1 -1 1
2 2
2 2


Output

1.0
-1.0
1.0


Input

5
0 1 3 6 10
3 10
2 3 4


Output

0.0
3.0
7.0
8.0
10.0

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll a[100010],ans[100010];
int c[100010],b[100010],d[100010];
int main() {
    int n; scanf("%d",&n);
    int i; ll sum=0; for(i=1;i<=n;i++) { scanf("%lld",&a[i]); a[i]-=sum; sum+=a[i]; c[i]=i; }
    int m; ll k; scanf("%d%lld",&m,&k); int x; for(i=1;i<=m;i++) { scanf("%d",&x); swap(c[x],c[x+1]); }
    for(i=1;i<=n;i++) if(!b[i]) { int cnt=0; int j; for(j=i;!b[j];j=c[j]) { b[j]=1; d[++cnt]=j; } for(j=1;j<=cnt;j++) ans[d[j]]=a[d[(j+k-1)%cnt+1]]; }
    for(i=1;i<=n;i++) { ans[i]+=ans[i-1]; printf("%lld.0\n",ans[i]); }
    return 0;
}