Upper bound of result of ANDing 2-intervals.

        :param a: Lower bound of first interval
        :param b: Upper bound of first interval
        :param c: Lower bound of second interval
        :param d: Upper bound of second interval
        :param w: bit width
        :return: Upper bound of ANDing 2-intervals

def max_and(a, b, c, d, w):
        """
        Upper bound of result of ANDing 2-intervals.

        :param a: Lower bound of first interval
        :param b: Upper bound of first interval
        :param c: Lower bound of second interval
        :param d: Upper bound of second interval
        :param w: bit width
        :return: Upper bound of ANDing 2-intervals
        """
        m = (1 << (w - 1))
        while m != 0:
            if ((~d) & b & m) != 0:
                temp = (b & ~m) | (m - 1)
                if temp >= a:
                    b = temp
                    break
            elif (d & (~b) & m) != 0:
                temp = (d & ~m) | (m - 1)
                if temp >= c:
                    d = temp
                    break
            m >>= 1
        return b & d