def get_primes(n):
    a = [True] * n
    for i in range(3, int(n**0.5)+1, 2):
        if a[i]:
            a[i**2::i*2] = [False] * int(((n-i**2-1)/(i*2)+1))
    return [2] + [i for i in range(3, n, 2) if a[i]]

def waiter(number, q):
    result, primes = [], get_primes(9734)
    for i in range(q + 1):
        b = number if i == q else [number.pop(j) for j in range(len(number) - 1, -1, -1) if number[j] % primes[i] == 0]
        result += b if i % 2 else b[::-1]
    return result

public static List<Integer> waiter(List<Integer> number, int q) {
        List<Integer> results = new ArrayList<>();
        
        // Find max value in the numbers list
        int max = number.stream().max( Integer::compareTo ).orElse(2) ;
        List<Integer> primes = sieveOfAtkin( max ) ;
          
        Stack<Integer> ai = new Stack<>();
        Stack<Integer> bi = new Stack<>();
        
        for(int k=0; k<q; ++k ) {
            if (k<primes.size()) {
                Integer prime = primes.get(k);
                System.out.println("prime: "+prime) ;
          
                while(!number.isEmpty()) {
                    Integer value = number.remove(number.size()-1);
                    if (value%prime == 0)
                        bi.push(value);
                    else
                        ai.push( value );
                }
                stackToList(bi,results );
                number.addAll(ai) ;
                ai.clear();
            } else {
                
                // All of the rest of the primes numbers are larger 
                // then any value in the number list. Just need to calculate 
                // the number of value reversals.
                if ( (q-k)/2 == 0 )
                    Collections.reverse(number);
                break;
            }
        }

        Collections.reverse(number);
        results.addAll(number);
        
        return results;
    }
    
    private static void stackToList(Stack<Integer> stack, List<Integer> list) {
        while(!stack.isEmpty()) {
            list.add(stack.pop()) ;
        }
    }

    /**
     * Creates a list of Prime numbers.
     * Based off of Sieve Of Atkin algorithm
     * 
     * @param limit - top possible prime number
     * @return List of prime numbers from 2 too limit inclusive.
     */
    private static List<Integer> sieveOfAtkin( final int limit ) {
        List<Integer> primes = new ArrayList<>();
        boolean[] sieve = new boolean[limit+1] ;
        
        // Special case calculations
        if ( sieve.length > 2 )
            sieve[2] = true;
        if ( sieve.length > 3 )
            sieve[3] = true;

        // Caching each case 
        for ( int x=1; x*x <= limit; ++x ) {
            for ( int y=1; y*y <=limit; ++y ) {
                int xx = x*x;
                int yy = y*y;
                    
                int n = (4*xx)+yy;
                if (n<=limit && ( n % 12==1 || n % 12==5 ))
                    sieve[n] ^= true;
                
                n = (3*xx)+yy;
                if (n<=limit && ( n % 12==7 ))
                    sieve[n] ^= true;
                
                n = (3*xx)-yy ;
                if ( x > y && n <= limit && n % 12 == 11 )
                    sieve[n] ^= true;
            }
        }
        
        // Marking multiples out 
        for ( int r = 5; r*r <=limit; ++r ) {
            if (sieve[r]) {
                for ( int i = r*r; i<= limit; i += r*r ) {
                    sieve[i] = false;
                }
            }
        }
        
        for ( int i = 2; i <= limit; ++i ) {
            if (sieve[i])
                primes.add(i) ;
        }
        
        return primes;
    }