  We present high-spatial-resolution ($\sim 0.12''$ or $\approx 800 \, {\rm
pc}$ at $z = 4.5$) ALMA $870\,\mu$m dust continuum observations of a sample of
44 ultrared dusty star-forming galaxies (DSFGs) selected from the H-ATLAS and
HerMES far-infrared surveys because of their red colors from 250 to 500 $\mu$m:
$S_{500} / S_{250} > 1.5$ and $S_{500} / S_{350} > 1.0$. With photometric
redshifts in the range $z \sim 4$-6, our sample includes the most luminous
starbursting systems in the early Universe known so far, with total obscured
star-formation rates (SFRs) of up to $\sim 4,500 \, M_\odot \, {\rm yr}^{-1}$,
as well as a population of lensed, less intrinsically luminous sources. The
lower limit on the number of ultrared DSFGs at 870 $\mu$m (with flux densities
measured from the ALMA maps and thus not affected by source confusion) derived
in this work is in reasonable agreement with models of galaxy evolution,
whereas there have been reports of conflicts at 500 $\mu$m (where flux
densities are derived from SPIRE). Ultrared DSFGs have a variety of
morphologies (from relatively extended disks with smooth radial profiles, to
compact sources, both isolated and interacting) and an average size,
$\theta_{\rm FWHM}$, of $1.46 \pm 0.41\, {\rm kpc}$, considerably smaller than
the values reported in previous work for less-luminous DSFGs at lower
redshifts. The size and the estimated gas-depletion times of our sources are
compatible with their being the progenitors of the most massive, compact,
red-and-dead galaxies at $z \sim 2$-3, and ultimately of local ultra-massive
elliptical galaxies or massive galaxy clusters. We are witnessing the birth of
the high-mass tail of the red sequence of galaxies.
