CF980B Marlin

The city of Fishtopia can be imagined as a grid of $ 4 $ rows and an odd number of columns. It has two main villages; the first is located at the top-left cell $ (1,1) $ , people who stay there love fishing at the Tuna pond at the bottom-right cell $ (4, n) $ . The second village is located at $ (4, 1) $ and its people love the Salmon pond at $ (1, n) $ . The mayor of Fishtopia wants to place $ k $ hotels in the city, each one occupying one cell. To allow people to enter the city from anywhere, hotels should not be placed on the border cells. A person can move from one cell to another if those cells are not occupied by hotels and share a side. Can you help the mayor place the hotels in a way such that there are equal number of shortest paths from each village to its preferred pond?

The first line of input contain two integers, $ n $ and $ k $ ( $ 3 \leq n \leq 99 $ , $ 0 \leq k \leq 2\times(n-2) $ ), $ n $ is odd, the width of the city, and the number of hotels to be placed, respectively.

Print "YES", if it is possible to place all the hotels in a way that satisfies the problem statement, otherwise print "NO". If it is possible, print an extra $ 4 $ lines that describe the city, each line should have $ n $ characters, each of which is "\#" if that cell has a hotel on it, or "." if not.