private class Node
    {
        public PrimeFactor pFactor;         // prime factor
        public Node next;
        public Node previous;
        /**
         * Default constructor for creating a dummy node.
         */
        public Node()
        {

        }

        /**
         * Precondition: p is a prime
         *
         * @param p  prime number
         * @param m  multiplicity
         * @throws IllegalArgumentException if m < 1
         */
        public Node(int p, int m) throws IllegalArgumentException
        {
            if(m < 1) {
                throw new IllegalArgumentException();
            }
                pFactor = new PrimeFactor(p,m);
        }

        /**
         * Constructs a node over a provided PrimeFactor object.
         *
         * @param pf
         * @throws IllegalArgumentException
         */
        public Node(PrimeFactor pf)
        {
            pFactor = new PrimeFactor(pf.prime, pf.multiplicity);
        }

        /**
         * Printed out in the form: prime + "^" + multiplicity.  For instance "2^3".
         * Also, deal with the case pFactor == null in which a string "dummy" is
         * returned instead.
         */
        @Override
        public String toString()
        {
            String X = "";
            if(pFactor == null) {
                 X = "dummy";
            }
            else{
                if(pFactor.multiplicity == 1) {
                X = pFactor.prime + "";
                }
                else {
                X = pFactor.prime + "^" + pFactor.multiplicity;
                }
            }
            return X;
        }
    }