  A dynamical model for large near-Earth asteroids (NEAs) is developed here to
understand the occurrence rate and nature of Cretaceous-Paleogene (K/Pg) scale
impacts on the Earth. We find that 16--32 (2--4) impacts of diameter $D>5$ km
($D>10$ km) NEAs are expected on the Earth in 1 Gyr, with about a half of
impactors being dark primitive asteroids (most of which start with semimajor
axis $a>2.5$ au). These results explain why the Chicxulub crater, the third
largest impact structure found on the Earth (diameter $\simeq180$ km), was
produced by impact of a carbonaceous chondrite. They suggest, when combined
with previously published results for small ($D \lesssim 1$ km) NEAs, a
size-dependent sampling of the main belt. We conclude that the impactor that
triggered the K/Pg mass extinction $\simeq 66$ Myr ago was a main belt asteroid
that quite likely ($\simeq 60$\% probability) originated beyond 2.5 au.
