AT_abc430_b [ABC430B] Count Subgrid

There is a grid with $ N $ rows and $ N $ columns. The cell at the $ i $ -th row from the top and $ j $ -th column from the left is painted black if $ S_{i,j} $ is `#`, and white if it is `.`. How many distinct patterns of painted cells can be obtained by extracting a region of $ M $ rows and $ M $ columns from this grid?

The input is given from Standard Input in the following format: > $ N $ $ M $ $ S_{1,1}\ldots S_{1,N} $ $ \vdots $ $ S_{N,1}\ldots S_{N,N} $

Print the answer.

### Sample Explanation 1 The state of the given grid is as shown in the left figure below. There are four ways to extract a region of two rows and two columns from this grid as shown in the right figure below, and there are three distinct patterns of painted cells.  ### Constraints - $ 1\leq M \leq N \leq 10 $ - $ N $ and $ M $ are integers. - $ S_{i,j} $ is `.` or `#`.