One day Mirko was cleaning up his room and found a straightedge and a compass. He went to the school the next day and challenged his friend Slavko to a geometric construction battle. Mirko knows how to construct some angles using the straightedge and compass and knows how to subtract and add any two angles he constructs. Slavko now shouts random angles and Mirko must draw them as fast as possible.
You are observing this battle and would like to know if Mirko can construct the angles Slavko shouts at all.
The first line of input contains two integers, , number of angles Mirko knows how to construct initially and , number of angles Slavko selected.
The second line of input contains integers, all smaller than , the angles Mirko knows how to construct initially.
The third line contains integers, all smaller than , the angles Slavko selected.
Output consists of lines, one for each angle Slavko selected. The -th line
YES if Mirko can construct the -th angle, and
Sample Input 1
2 1 30 70 40
Sample Output 1
Explanation for Sample Output 1
Subtracting from yields .
Sample Input 2
1 1 100 60
Sample Output 2
Explanation for Sample Output 2
Adding times yields , also known as .
Sample Input 3
3 2 10 20 30 5 70
Sample Output 3