In this paper, we study the achievable degrees of freedom (DoFs) for K -user multiple-input single-output broadcast channel (BC) in the absence of channel state information at the transmitter under the finite channel coherent time. For the considered K-user BC, a transmitter is equipped with multiple conventional antennas, and receivers are equipped with a reconfigurable antenna that is capable of dynamically modifying the receiving beam radiation pattern. In this system, we propose a blind interference alignment scheme that is able to allocate an asymmetric number of information symbols to each user, which is essentially required to improve DoFs under limited symbol extension. A generalized systematic construction method of transmit beamforming vectors and receiving mode selection patterns to deal with such asymmetric allocation is established. As a consequence, for a broad class of network configurations and symbol extension constraints, the proposed scheme attains an improved sum DoF compared to the previous works, allowing only for the same number of information symbols for all users.