Problem K - World Finals Warmup Occidental Contest

Problem K

The Great Divide

Input: standard input

Output: standard output

Time Limit: 8 seconds

Memory Limit: 32 MB

Somewhere in Gaul, there is a little village very like the village where Asterix and Obelix live. Not very long ago they had only one chief Altruistix and peace reigned in the village. But now those happy days are just dreams. The villagers are now divided. Some of the villagers have elected Majestix as their chief and the others have elected Cleverdix.

Majestix Cleverdix

The two chiefs have decided to divide the village into two parts by digging a straight ditch through the middle of the village so that the houses of the supporters of Majestix lie on one part and those of the followers of Cleverdix lie on the other. So, they have invited Getafix, the venerable druid of Asterix’s village, to figure out whether such a dividing line exists or not.

Getafix

Since Getafix knows that you are so good in programming, he seeks your help.

Input

The input may contain multiple test cases.

The first line of each test case contains two integers M and C (1 £ M, C £ 500), indicating the number of houses of the supporters of Majestix and Cleverdix respectively.

Each of the next M lines contains two integers x and y (-1000 £ x, y £ 1000) giving the co-ordinates of the house of a supporter of Majestix. For convenience each house is considered as a single point on the plane.

Each of the next C lines contains two integers x and y (-1000 £ x, y £ 1000) giving the co-ordinates of the house of a supporter of Cleverdix.

The input will terminate with two zeros for M and C.

Output

For each test case in the input output a line containing either “Yes” or “No” depending on whether there exists a straight line that divides the two set of houses. The dividing line can NOT contain points of both sides.

Sample Input

4 3

100 600

200 400

600 500

300 700

400 100

600 200

500 300

4 3