Cylon Code

The battlestar Galactica intercepted a message from the Cylons. The message is an integer matrix $A$ of size $n \times m$, and it is encoded. After interrogating one of the Cylon sixes, the crew learned how the matrix is encoded. A $2 \times 2$ matrix $C$ is used. Each element of $C$ is an integer with absolute value at most 1, and $C_{22} \neq 0$. When matrix $B$ is encoded, the result is a matrix $A$ with the same size as $B$, where $A_{ij} = B_{i-1,j-1} \cdot C_{11} + B_{i-1,j} \cdot C_{12} + B_{i,j-1} \cdot C_{21} + B_{ij} \cdot C_{22}$ If an index falls outside the matrix, that element is taken to be zero. Admiral Adama asks you to decode the Cylon message, since the fate of what remains of humanity depends on it.

The first line contains two integers $n$ and $m$ ($1 \le n,m \le 20$). The next $n$ lines each contain $m$ integers, which form the encoded matrix $A$. The number in the $j$-th position of the $(i+1)$-th line is $A_{ij}$. The last line contains four integers $C_{11}$, $C_{12}$, $C_{21}$, and $C_{22}$, the elements of matrix $C$. All numbers in the input are integers with absolute value at most 1000. For all $i$ and $j$, $|C_{ij}| \le 1$, and $C_{22} \neq 0$.

Print $n$ lines with $m$ numbers each. These are the elements of the matrix $A$ decoded with matrix $C$.