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?

菲什托皮亚城可以被想象成一个 $4$ 行、奇数列的网格。该城有两个主要村庄：第一个村庄位于左上角单元格 $(1,1)$，居住在此的人们喜爱在右下角单元格 $(4, n)$ 的金枪鱼池垂钓；第二个村庄位于 $(4, 1)$，其居民则喜爱位于 $(1, n)$ 的鲑鱼池。

菲什托皮亚市长希望在城中放置 $k$ 家酒店，每家酒店占据一个单元格。为允许人们从任意边界位置进入城市，酒店不得建在边界单元格上。

当两个单元格未被酒店占据且有公共边时，人们可在这两个单元格之间移动。

您能否帮助市长安排这些酒店的位置，使得从每个村庄到其对应偏爱池塘的最短路径数目相等？

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.

输入的第一行包含两个整数 $n$ 和 $k$（$3 \leq n \leq 99$，$0 \leq k \leq 2\times(n-2)$），其中 $n$ 为奇数，表示城市的宽度，$k$ 表示需放置的酒店数量。

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.

如果可以按题目要求的方式放置所有酒店，则输出 "YES"，否则输出 "NO"。

如果可以实现，则额外输出 $4$ 行来描述该城市，每行包含 $n$ 个字符：若该位置有酒店，则对应字符为 "#"；否则为 "."。