A hybrid experiment consisting of emulsion chambers, burst detectors and the Tibet II air-shower array was carried out at Yangbajing (4,300 m a.s.l., 606 g/cm$^2$) in Tibet to obtain the energy spectra of primary protons and heliums. From three-year operation, these energy spectra are deduced between $10^{15}$ and $10^{16}$ eV by triggering the air showers associated with a high energy core and using a neural network method in the primary mass separation. The proton spectrum can be expressed by a single power-law function with a differential index of $-3.01 pm 0.11$ and $-3.05 pm 0.12$ based on the QGSJET+HD and SIBYLL+HD models, respectively, which are steeper than that extrapolated from the direct observations of $-2.74 pm 0.01$ in the energy range below $10^{14}$ eV. The absolute fluxes of protons and heliums are derived within 30% systematic errors depending on the hadronic interaction models used in Monte Carlo simulation. The result of our experiment suggests that the main component responsible for the change of the power index of the all-particle spectrum around $3 times 10^{15}$ eV, so-called ``knee, is composed of nuclei heavier than helium. This is the first measurement of the differential energy spectra of primary protons and heliums by selecting them event by event at the knee energy region.
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