You are a waiter at a party. There is a pile of numbered plates. Create an empty $\textit{answers}$ array. At each iteration, $\boldsymbol{i}$, remove each plate from the top of the stack in order. Determine if the number on the plate is evenly divisible by the $i^t h$ prime number. If it is, stack it in pile $B_i$. Otherwise, stack it in stack $A_i$. Store the values in $B_i$ from top to bottom in $\textit{answers}$. In the next iteration, do the same with the values in stack $A_i$. Once the required number of iterations is complete, store the remaining values in $A_i$ in $\textit{answers}$, again from top to bottom. Return the $\textit{answers}$ array.

Example

$A=[2,3,4,5,6,7]$

$q=3$

An abbreviated list of primes is $[2,3,5,7,11,13]$. Stack the plates in reverse order.

$A_0=[2,3,4,5,6,7]$

$\textit{answers}=[]$

Begin iterations. On the first iteration, check if items are divisible by $2$.

$A_1=[7,5,3]$

$B_1=[6,4,2]$

Move $\begin{array}{c}B_1\end{array}$ elements to $\textit{answers}$.

$answers=[2,4,6]$

On the second iteration, test if $\boldsymbol{A_1}$ elements are divisible by $3$.

$A_2=[7,5]$

$B_2=[3]$

Move $B_2$ elmements to $\textit{answers}$.

$answers=[2,4,6,3]$

And on the third iteration, test if $\boldsymbol{A_{2}}$ elements are divisible by $5$.

$A_{3}=[7]$

$B_3=[5]$

Move $B_2$ elmements to $\textit{answers}$.

$answers=[2,4,6,3,5]$

All iterations are complete, so move the remaining elements in $A_3$, from top to bottom, to $\textit{answers}$.

$answers=[2,4,6,3,5,7]$. Return this list.

Function Description

Complete the waiter function in the editor below.

waiter has the following parameters:

int number[n]: the numbers on the plates
int q: the number of iterations

Returns

int[n]: the numbers on the plates after processing

Input Format

The first line contains two space separated integers, $n$ and $\textit{q}$.

The next line contains $n$ space separated integers representing the initial pile of plates, i.e., $\mbox{A}$.

Constraints

$1\leq n\leq5\times10^4$

$2\leq{number[i]}\leq{10^4}$

$1\leq q\leq1200$

Sample Input 0
5 1
3 4 7 6 5

Sample Output 0
4
6
3
7
5

Explanation 0

Initially:

$\mbox{A}$ = [3, 4, 7, 6, 5]<-TOP

After 1 iteration (divide by 2, the 1st prime number):

$\boldsymbol{A_1}$ = [5, 7, 3]<-TOP

$\begin{array}{c}B_1\end{array}$ = [6, 4]<-TOP

Move $\begin{array}{c}B_1\end{array}$ elements to $\textit{answers}$.

$answers=[4,6]$

All iterations are complete, so move $\boldsymbol{A_1}$ elements to $\textit{answers}$.

$answers=[4,6,3,7,5]$.

Sample Input 1
5 2
3 3 4 4 9

Sample Output 1
4
4
9
3
3

Explanation 1

Initially:

$\mbox{A}$ = [3, 3, 4, 4, 9]<-TOP

After $1^{st}$ iteration (divide by 2):

$\boldsymbol{A_1}$ = [9, 3, 3]<-TOP

$\begin{array}{c}B_1\end{array}$ = [4, 4]<-TOP

Move $\begin{array}{c}B_1\end{array}$ to $\textit{answers}$.

$a n s wers=[4,4]$

After $2^{nd}$ iteration (divide by 3):

$\boldsymbol{A_{2}}$ = []<- TOP

$B_2$ = [3, 3, 9]<-TOP

Move $B_2$ elements to $\textit{answers}$.

$answers=[4,4,9,3,3]$

There are no values remaining in $\boldsymbol{A_{2}}$.

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