  Precise measurements of galactic cosmic rays revealed a significant
difference between the rigidity spectral indices of protons and helium ions.
This finding is a notable contrast to the commonly accepted theoretical
prediction that supernova remnant (SNR) shocks accelerate protons and helium
ions with the same rigidity alike. Most of the earlier explanations for the
"paradox" appealed to SNR environmental factors, such as inhomogeneous $p$/He
mixes in the shock upstream medium, variable ionization states of He, or a
multi-SNR origin of the observed spectra. The newest observations, however, are
in tension with most of them. In this paper, we show by self-consistent hybrid
simulations that such special conditions are not vital for the explanation of
the cosmic ray rigidity spectra. In particular, our simulations prove that an
SNR shock can modify the chemical composition of accelerated cosmic rays by
preferentially extracting them from a homogeneous background plasma without
additional, largely untestable assumptions. Our results confirm the earlier
theoretical predictions of how the efficiency of injection depends on the shock
Mach number $M.$ Its increase with the charge-to-mass ratio saturates at a
level that grows with $M.$ We have convolved the time-dependent injection rates
of protons and helium ions, obtained from the simulations, with a decreasing
shock strength over the active life of SNRs. The integrated SNR rigidity
spectrum for $p$/He ratio compares well with the AMS-02 and PAMELA data.
