  We explore magnetic-field amplification due to the Kelvin-Helmholtz
instability during binary neutron star mergers. By performing high-resolution
general relativistic magnetohydrodynamics simulations with a resolution of
$17.5$ m for $4$--$5$ ms after the onset of the merger on the Japanese
supercomputer "K", we find that an initial magnetic field of moderate maximum
strength $10^{13}$ G is amplified at least by a factor of $\approx 10^3$. We
also explore the saturation of the magnetic-field energy and our result shows
that it is likely to be $\gtrsim 4 \times 10^{50}$ erg, which is $\gtrsim
0.1\%$ of the bulk kinetic energy of the merging binary neutron stars.
