Problem Statement

Euler's bloodline has a secret rule that all descendants must choose their favourite number once they turn $18.$ But if you are a descendant of one the world's greatest Mathermaticians, you are not allowed to choose any random number right?

Aleksandra is turning $18$ next month, but the problem is she is very bad at Math. So she approaches you with the conditions to choose a favourite number for her. The secret rule is that the chosen number must be a Parent Mask or Child Mask of at least one of the numbers listed down in a secret scroll passed through generations. Parent Mask of number X is defined as a number that can be obtained by flipping zero or more unset bits of X$.$ Similarly Child Mask of X can be obtained by flipping zero or more set bits of X$.$ As a reminder, set bits refer to $1$s in the binary representation of the number and unset bits refer to the Os in its binary representation.

For example $3(11$ in binary$)$ is a Parent Mask of $2(10$ in binary$)$ as we can change the Least Significant bit of $2$ from $0$ to $1.$ By similar logic, $2$ is a Child Mask of $3.$

Written more formally:

Parent Mask$($X$)$&X$=$X

ChiMask $($X$)$ & X Child Mask$($X$)$

where & represents bitwise AND operator Note that an integer X is both Parent Mask and Child Mask of itself.

As stated before, Aleksandra is bad at mathematics$($her family's genes missed her$)$ so she stole the secret scroll with the list of numbers and gave it to you. The scroll contains N numbers Az$.$ Az

AN Aleksandra has Q queries, each containing a single integer X Your task is to determine if X can potentially be

Aleksandra's favourite number or not. In short, determine if X is either a Parent Mask or Child Mask of at least one of the numbers A$1,$ A$2,.....,$ AN$.$

Input Format:

$$ The first line contains two space separated integers N and Q$.$ denoting the count of numbers in the secret scroll and the number of queries Aleksandra has respectively.

$$ Second line contains N space separated integers A$1,$ A$2,.......$ AN$,$ the numbers as mentioned in the secret scroll.

$$ The next Q lines each contain a number X which Aleksandra wants to know if it can be her favourite number or not.

Constraints:

$2<=$N$<=10$ power $6$

$1<=$Q$<=10$ power $5$

$0<=$Ai$<=10$ power $6$

$0<=$X$<=10$ power $6$

Output:

$$ Print "Yes" or $"$No$"($case sensitive$)$ depending on if X can be Aleksandra's favourite number or not.

$$

Sample input:

$23$

$13$

$2$

$4$

$5$

Sample output:

Yes

No

Yes

Sample output explanation:

The scroll contains the numbers $1$ and $3$ here.

$1$ The first query, $2$subscrit$10$ is a child mask of $3$subacript$10,$ since $3$subscript$10$ in binary is $112$ and we can flip the last bit to obtain $10,$ which is $2$subscipt$10$ decimal.

$2.$ It can similarly be seen that $4$subscript$10(1002$ in binary$)$ is neither parent mask nor a child mask of both $110$ and $3$subscripy$10-$

$3.5$subscript$10(1012)$ on the other hand is a parent mask of $1$subacript$10(1$subscript$2).$

Note that the subscript $2$ means binary and subscript $10$ mean decimal as usual.