It is crucial to detect potential overlaps between any pair of the input reads and a reference genome in genome sequencing, but it takes an excessive amount of time, especially for ultra-long reads. Even though lots of acceleration designs are proposed for different sequencing methods, several crucial drawbacks impact these methods. One of these difficulties stems from the difference in read lengths that may take place as input data. In this work, we propose a new Race-logic implementation of the seed extension kernel of the BWA-MEM alignment algorithm. The first proposed method does not need reconfiguration to execute the seed extension kernel for different read lengths. We use MEMRISTORs instead of the conventional, complementary metal-oxide-semiconductor (CMOS), which leads to lower area overhead and power consumption. Also, we benefit from Field-Programmable Nanowire Interconnect Architecture as our matrix output resulting in a flexible output that bypasses the reconfiguration procedure of the system for reads with different lengths. Considering the power, area, and delay efficiency, we gain better results than other state-of-the-art implementations. Consequently, we gain up to 22x speedup compared to the state-of-the-art systolic arrays, 600x speed up considering different seed lengths of the previous state-of-the-art proposed methods, at least 10x improvements in area overhead, and 105x improvements in power.