/**
     * Updates n to its p-th power modulo m.
     *
     * @param n
     *            number to be raised to a power
     * @param p
     *            the power
     * @param m
     *            the modulus
     * @updates n
     * @requires m > 1
     * @ensures n = #n ^ (p) mod m
     */
    public static void powerMod(NaturalNumber n, NaturalNumber p,
            NaturalNumber m) {
        assert m.compareTo(new NaturalNumber2(1)) > 0 : "Violation of: m > 1";

        /*
         * Use the fast-powering algorithm as previously discussed in class,
         * with the additional feature that every multiplication is followed
         * immediately by "reducing the result modulo m"
         */

        // TODO - fill in body
        NaturalNumber mod = new NaturalNumber2();
        mod = p.divide(new NaturalNumber2(2));

        if (p.equals(0)) {
            n.copyFrom(new NaturalNumber2(1));

        } else if (mod.isZero()) { //if p is even
            p.divide(new NaturalNumber2(2));

            p.multiply(new NaturalNumber2(2));
        } else if (!mod.isZero()) { //if p is odd
            p.divide(new NaturalNumber2(2));

            p.multiply(new NaturalNumber2(2));
            p.add(new NaturalNumber2(1));
        }

    }