Drazil and His Happy Friends
题意翻译
Drazil 有许多朋友，有一些人是乐观的，而其他人则不然（未必就是悲观的），她决定帮助她的朋友们。她的朋友，有 $n$ 个男生和 $m$ 个女生，编号分别是 $0$ ~ $n-1$ 和 $0$ ~ $m-1$ 。Drazil 决定第 i 天邀请第 ($i \bmod n$) 号男生和第 $j$($=i \mod m$) 号女生共进晚餐，（$i=0,1,……$）。Drazil觉得，乐观是可以传染的，即她认为如果有人是乐观的，那么与他（她）共进晚餐的另一个人也会变得乐观（当然，如果两个人都是乐观的或者都不是乐观的，则保持原样），而且这种状态也会保持下去。现在的问题是，Drazil想知道，这种办法能否在若干天后使得她的所有朋友都会变得乐观。
题目描述
Drazil has many friends. Some of them are happy and some of them are unhappy. Drazil wants to make all his friends become happy. So he invented the following plan.
There are $ n $ boys and $ m $ girls among his friends. Let's number them from $ 0 $ to $ n-1 $ and $ 0 $ to $ m-1 $ separately. In $ i $ -th day, Drazil invites -th boy and -th girl to have dinner together (as Drazil is programmer, $ i $ starts from $ 0 $ ). If one of those two people is happy, the other one will also become happy. Otherwise, those two people remain in their states. Once a person becomes happy (or if he/she was happy originally), he stays happy forever.
Drazil wants to know whether he can use this plan to make all his friends become happy at some moment.
输入输出格式
输入格式
The first line contains two integer $ n $ and $ m $ ( $ 1<=n,m<=100 $ ).
The second line contains integer $ b $ ( $ 0<=b<=n $ ), denoting the number of happy boys among friends of Drazil, and then follow $ b $ distinct integers $ x_{1},x_{2},...,x_{b} $ ( $ 0<=x_{i}<n $ ), denoting the list of indices of happy boys.
The third line conatins integer $ g $ ( $ 0<=g<=m $ ), denoting the number of happy girls among friends of Drazil, and then follow $ g $ distinct integers $ y_{1},y_{2},...\ ,y_{g} $ ( $ 0<=y_{j}<m $ ), denoting the list of indices of happy girls.
It is guaranteed that there is at least one person that is unhappy among his friends.
输出格式
If Drazil can make all his friends become happy by this plan, print "Yes". Otherwise, print "No".
输入输出样例
输入样例 #1
2 3
0
1 0
输出样例 #1
Yes
输入样例 #2
2 4
1 0
1 2
输出样例 #2
No
输入样例 #3
2 3
1 0
1 1
输出样例 #3
Yes
说明
By  we define the remainder of integer division of $ i $ by $ k $ .
In first sample case:
- On the 0-th day, Drazil invites 0-th boy and 0-th girl. Because 0-th girl is happy at the beginning, 0-th boy become happy at this day.
- On the 1-st day, Drazil invites 1-st boy and 1-st girl. They are both unhappy, so nothing changes at this day.
- On the 2-nd day, Drazil invites 0-th boy and 2-nd girl. Because 0-th boy is already happy he makes 2-nd girl become happy at this day.
- On the 3-rd day, Drazil invites 1-st boy and 0-th girl. 0-th girl is happy, so she makes 1-st boy happy.
- On the 4-th day, Drazil invites 0-th boy and 1-st girl. 0-th boy is happy, so he makes the 1-st girl happy. So, all friends become happy at this moment.