Hope you still have not forgotten about pig Benny.

She is asking for help again.

This time you have to answer some queries that Benny will give you.

All actions happen in the Universe where each planet has its own id starting from 0. There are infinite amount of planets.

To travel between different planets there are some special spacecrafts. Each spacecraft is characterized by the number d_i.

If the id of the planet you are currently staying on is id_j and you decided you use spacecraft with d_i you will go to planet with id equal to id_j + d_i.

Benny's parents live nearby the planet with id equal to 0, so you may assume that there exists some spacecraft for which d_i is not more than 10⁴.

You have to answer Q queries. Each query consists of one single integer x. You have to answer whether it's possible to go from planet with id equal to 0 to planet with id equal to x.

Constraints

1 <= N <= 10^3

1 <= Q <= 10^5

1 <= Di <= 10^9

1 <= X <= 10^9

Input

The first line contains two integers denoting N and Q.

The second line contains N integers denoting d_i for spacecrafts. Numbers might be separated with more than one space and not more than 10.

The following Q lines contain single integer denoting x_i.