{"raw_statement":[{"iden":"problem statement","content":"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 $x_i$.\nThe 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 $x$.\nThe 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."},{"iden":"constraints","content":"*   $3≤N≤10^5$\n*   $x_i$ is an integer.\n*   $|x_i|≤10^9$\n*   $1≤M≤10^5$\n*   $2≤a_j≤N-1$\n*   $1≤K≤10^{18}$"},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$x_1$ $x_2$ $...$ $x_N$\n$M$ $K$\n$a_1$ $a_2$ $...$ $a_M$"},{"iden":"sample input 1","content":"3\n-1 0 2\n1 1\n2"},{"iden":"sample output 1","content":"\\-1.0\n1.0\n2.0\n\nRabbit $2$ 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 $0.5×(-2)+0.5×4=1.0$."},{"iden":"sample input 2","content":"3\n1 -1 1\n2 2\n2 2"},{"iden":"sample output 2","content":"1.0\n-1.0\n1.0\n\n$x_i$ may not be distinct."},{"iden":"sample input 3","content":"5\n0 1 3 6 10\n3 10\n2 3 4"},{"iden":"sample output 3","content":"0.0\n3.0\n7.0\n8.0\n10.0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}