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 $10^{-9}$.