Milling machines

A fab lab is an open, small-scale workshop where you can create or fabricate almost anything you want mostly by using computer controlled tools like a laser cutter or a 3D printer. The FAU fab lab recently got a CNC milling machine. Using the milling machine you can cut or remove material with different tools from the surface of a workpiece. It is controlled via a computer program.

I sometimes wondered what happens if multiple different shaped workpieces are sent through the same milling program. For simplification assume that we have only two dimensional workpieces without holes. A milling program consists of multiple steps; each step describes where the milling machine has to remove material (using different tools) from the top of the surface.

Input

The first line consists of two integers $w$ and $s(1\le w,s\le 10^4)$, where $w$ gives the number of workpieces and $s$ the number of steps in the milling program. The next line consists of two integers $x$ and $y(1\le x,y\le 100)$, where $x$ gives the width and $y$ gives the maximal possible height of workpieces.

Then follow $w$ lines, each describing one workpiece. Each workpiece description consists of $x$ non-negative integers specifying the surface height in that column.

Then follow $s$ lines, each describing one milling step of the milling program. Each milling step description consists of $x$ non-negative integers $s_i(0\le s_i\le y)$ specifying the amount of surface to cut off in each column (relative to the height of the milling area, i.e. $y$, not relative to the top of the workpiece). See Figure for details.

Output

For each workpiece, output one line containing $x$ integers specifying the remaining surface heights (in the same order as in the input).

Examples

Second workpiece in first sample: initial workpiece followed by milling in each column — the value in the milling program determines the vertical position of the cutter head.