/** Returns a * b mod m. */
    abstract long mulMod(long a, long b, long m);

    /** Returns a^2 mod m. */
    abstract long squareMod(long a, long m);

    /** Returns a^p mod m. */
    private long powMod(long a, long p, long m) {
      long res = 1;
      for (; p != 0; p >>= 1) {
        if ((p & 1) != 0) {
          res = mulMod(res, a, m);
        }
        a = squareMod(a, m);