Switches and Lamps

题意翻译

题目大意： 输入n，m,n代表开关的个数，m代表灯的个数 就是给你一个矩阵，然后a[i][j]代表第i个灯能够控制第j个 灯，然后问题在去掉一个特定灯的条件下，能不能使剩下的 灯还全部能够被控制，如果有这样的一盏灯，就输出yes，如 果没有，就输出no。 感谢@历史——殿堂 提供的翻译

题目描述

You are given $ n $ switches and $ m $ lamps. The $ i $ -th switch turns on some subset of the lamps. This information is given as the matrix $ a $ consisting of $ n $ rows and $ m $ columns where $ a_{i,j}=1 $ if the $ i $ -th switch turns on the $ j $ -th lamp and $ a_{i,j}=0 $ if the $ i $ -th switch is not connected to the $ j $ -th lamp. Initially all $ m $ lamps are turned off. Switches change state only from "off" to "on". It means that if you press two or more switches connected to the same lamp then the lamp will be turned on after any of this switches is pressed and will remain its state even if any switch connected to this lamp is pressed afterwards. It is guaranteed that if you push all $ n $ switches then all $ m $ lamps will be turned on. Your think that you have too many switches and you would like to ignore one of them. Your task is to say if there exists such a switch that if you will ignore (not use) it but press all the other $ n-1 $ switches then all the $ m $ lamps will be turned on.

输入输出格式

输入格式

The first line of the input contains two integers $ n $ and $ m $ ( $ 1<=n,m<=2000 $ ) — the number of the switches and the number of the lamps. The following $ n $ lines contain $ m $ characters each. The character $ a_{i,j} $ is equal to '1' if the $ i $ -th switch turns on the $ j $ -th lamp and '0' otherwise. It is guaranteed that if you press all $ n $ switches all $ m $ lamps will be turned on.

输出格式

Print "YES" if there is a switch that if you will ignore it and press all the other $ n-1 $ switches then all $ m $ lamps will be turned on. Print "NO" if there is no such switch.

输入输出样例

输入样例 #1

4 5
10101
01000
00111
10000

输出样例 #1

YES

输入样例 #2

4 5
10100
01000
00110
00101

输出样例 #2

NO