There are $N$ students and intelligence of each student is given in the form of array $A$ . 

There are $Q$ queries.In each query Integer $X$ is given.For each query you have to print number of groups of students having strength greater than or equal to $X$. Strength of group is defined as bitwise $OR$ of intelligence of all the students present in that group.

$note$:- Two groups are said to be different if they have atleast one student which is not present in both groups.

Input:

First line contains $N$ and $Q$.

Second line contains $N$ integers where $ith$ integer denotes intelligence of $ith$ student.

Next $Q$ lines will contain $X$.

Output:

For each query you have to print number of groups of students having strength greater than or equal to $X$.

Constraints:

$1\leq N\leq 20$

$1\leq Q\leq 10^5$

$1\leq intelligence\leq 10^5$