@VisibleForTesting
  static int[] biggestBinomials = {
    Integer.MAX_VALUE,
    Integer.MAX_VALUE,
    65536,
    2345,
    477,
    193,
    110,
    75,
    58,
    49,
    43,
    39,
    37,
    35,
    34,
    34,
    33
  };

  /**
   * Returns the arithmetic mean of {@code x} and {@code y}, rounded towards negative infinity. This