Lower 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: Lower bound of ANDing 2-intervals

def min_and(a, b, c, d, w):
        """
        Lower 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: Lower bound of ANDing 2-intervals
        """
        m = (1 << (w - 1))
        while m != 0:
            if (~a & ~c & m) != 0:
                temp = (a | m) & -m
                if temp <= b:
                    a = temp
                    break
                temp = (c | m) & -m
                if temp <= d:
                    c = temp
                    break
            m >>= 1
        return a & c