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Half-cycle terahertz pulse generation in a super-intense laser radiation interaction with a nanostructured target consisting of nanowires or nanofoil stripes is studied. During propagation of a relativistic laser pulse along a nanowire (longitudinal interaction), dense high-charge bunches of electrons are forced out of the target and accelerated in the laser field, generating high-power electromagnetic radiation with various spectral composition including terahertz and infrared ranges. For a relatively long laser pulse (tens or hundreds of femtoseconds) with a smooth shape, nanowire electrons are displaced from the target by each laser half cycle. In this case, the low-frequency part of the generated radiation can have a unipolar half-cycle shape with characteristics determined by the laser and target parameters. Such a shape of radiation allows to add coherently emission from different target nanowires inside the laser spot. Due to nanometer scale transverse dimensions of the nanowire, laser field amplitude decreases only in its vicinity after interaction. Then a spatially rich nanostructured target formed by parallel nanowires each using its own part of the laser front can produce stronger radiation. Also, for a relatively long laser pulse, its amplitude decreases when interacting with the nanowire only for the first few periods. In this case, consecutive interaction of a laser pulse with nanowires can be used, and the nanostructured target can be formed from the consecutive nanowires. Moreover, using several regularly located nanowires (or nanofoil stripes), one can engineer the shape of the generated radiation pulse or even produce a train of half-cycle terahertz or infrared pulses with controlled delay between them.