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Giant second-harmonic generation in the terahertz (THz) frequency range is observed in a thin film of an s-wave superconductor NbN, where the time-reversal (T) and space-inversion (P) symmetries are simultaneously broken by supercurrent injection. We demonstrate that the phase of the second-harmonic signal flips when the direction of supercurrent is inverted; i.e., the signal is ascribed to the nonreciprocal response that occurs under broken P and T symmetries. The temperature dependence of the SH signal exhibits a sharp resonance, whi