codeforce 980B

Marlin

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

The city of Fishtopia can be imagined as a grid of $\mathrm{44 rows\; and\; an odd number\; of\; columns.\; It\; has\; two\; main\; villages;\; the\; first\; is\; located\; at\; the\; top-left\; cell (1,1)(1,1),\; people\; who\; stay\; there\; love\; fishing\; at\; the\; Tuna\; pond\; at\; the\; bottom-right\; cell (4,n)(4,n).\; The\; second\; village\; is\; located\; at (4,1)(4,1) and\; its\; people\; love\; the\; Salmon\; pond\; at (1,n)(1,n).}$

The mayor of Fishtopia wants to place $\mathrm{kk hotels\; in\; the\; city,\; each\; one\; occupying\; one\; cell.\; To\; allow\; people\; to\; enter\; the\; city\; from\; anywhere,\; hotels\; should\; not\; be\; placed\; on\; the\; border\; cells.}$

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?

Input

The first line of input contain two integers, $\mathrm{nn and kk (3\le n\le 993\le n\le 99, 0\le k\le 2\times (n-2)0\le k\le 2\times (n-2)), nn is odd,\; the\; width\; of\; the\; city,\; and\; the\; number\; of\; hotels\; to\; be\; placed,\; respectively.}$

Output

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 $\mathrm{44 lines\; that\; describe\; the\; city,\; each\; line\; should\; have nn characters,\; each\; of\; which\; is\; "\#"\; if\; that\; cell\; has\; a\; hotel\; on\; it,\; or\; "."\; if\; not.}$

Examples

input

Copy

7 2

output

Copy

YES
.......
.#.....
.#.....
.......

input

Copy

5 3

output

Copy

YES
.....
.###.
.....
.....

这是一道天坑题，不存在NO的情况，都是YES;

所以如果K是偶数就先放左边，如果K是奇数就从中间开始放；

题意：

有一个城市有4行n列，n是奇数，有一个村庄在(1,1)，村民的活动地点是(4,n)；

有一个村庄在(4,1)，村民的活动地点是(1,n)；

现在要修建k个宾馆，不能修建在边界上，问能否给出一种安排方案使得两个村庄的村民到他们各自的活动地点的最短路的条数相等。

思路：

画了几个实例就应该知道，无论n和k是多少，都可以构建出合理的方案，所以全是YES。

如果k为偶数，那么就上下对称，这个比较好构造；当k为奇数，我采用的是首先把第二排从中间开始向两边填满，然后第三排则是从中间一格的两边开始填。

#include<stdio.h>
#include<string.h>
#include<string>
#include<iostream>
#include<string.h>
#include<algorithm>
#include<vector>
#include<stdio.h>
#include<cstdio>
#include<time.h>
#include<stack>
#include<queue>
#include<deque>
#define inf 0x3f3f3f3f
#define ll long long
using namespace std;
char a[5][105];
int main()
{
   int n,k;
   cin>>n>>k;
   cout<<"YES"<<endl;
   if(k%2==0)
   {
       for(int i=2;i<=k/2+1;i++)
       {
           a[2][i]='#';
           a[3][i]='#';
       }
   }
   else
   {
       if(k<=n-2)
       {
           int p=n/2+1;
            int l=1,r=0;
            for(int i=1;i<=k;i++)
           {
               if(i%2==1) 
               {
                   a[2][p+r]='#';
                   r++;
               }
               else 
               {
                   a[2][p-l]='#';
                   l++;
               }
           }
       }
       else
       {
           for(int i=2;i<=n-1;i++)
           {
               a[2][i]='#';
           }
           k=k-n+2;
           int l=1,r=2;
           for(int i=1;i<=k;i++)
           {
               if(i%2==1) 
               {
                   a[3][r]='#';
                   r++;
               }
               else 
               {
                   a[3][n-l]='#';
                   l++;
               }
           }
       }
   }
   for(int i=1;i<=4;i++)
   {
       for(int j=1;j<=n;j++)
       {
           if(a[i][j]!='#') a[i][j]='.';
           else s++;
           cout<<a[i][j];
       }
       cout<<endl;
   }
   return 0;
}