Codeforces Round 292 (Div. 2) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

brute force

dsu

meet-in-the-middle

number theory

*1300

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Drazil and His Happy Friends

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputDrazil 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.

Input

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.

Output

If Drazil can make all his friends become happy by this plan, print "Yes". Otherwise, print "No".

Examples

Input

2 3

0

1 0

Output

Yes

Input

2 4

1 0

1 2

Output

No

Input

2 3

1 0

1 1

Output

Yes

Note

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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Apr/22/2024 18:12:07 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|