  We study X-ray and soft gamma-ray spectra from the hard state of the
accreting black-hole binary MAXI J1820+070. We perform analysis of two joint
spectra from NuSTAR and INTEGRAL, covering the range of 3--650 keV and of an
average joint spectrum over the rise of the hard state, covering the 3--2200
keV range. The spectra are well modelled by Comptonization of soft seed
photons. However, the distributions of the scattering electrons are not purely
thermal; we find they have substantial high-energy tails, well modelled as
steep power laws. The corresponding power-law photon tail in the average
spectrum is detected well beyond the threshold for electron-positron pair
production, 511 keV. This allows us to calculate the rate of the
electron-positron pair production and put a lower limit on the size of the
source from pair equilibrium of 3--4 gravitational radii. If we adopt the sizes
estimated by us from the reflection spectroscopy of $>$20 gravitational radii,
the fractional pair abundance becomes much less than unity. The low pair
abundance is confirmed by the lack of an annihilation feature in the average
spectrum.
