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Today, the brightest cluster galaxies (BCGs) are passive and very massive galaxies at the center of their clusters, and they still accrete mass through swallowing companions and gas from cooling flows. However their formation history is not well known. We report CO(4$\rightarrow$3) and continuum map observations of the SpARCS1049+56 BCG at $z=1.709$, one of the most distant known BCGs. Our observations yield $M_{{\rm H}_2}<1.1\times10^{10}M_\odot$ for the BCG; while in CO(4$\rightarrow$3), we detect two gas-rich companions at the northeast and southeast of the BCG, within 20 kpc, with ${L^\prime_{\rm CO(4\rightarrow3)}=(5.8\pm0.6)\times10^{9}}$ K km s$^{-1}$ pc$^2$ and $(7.4\pm0.7)\times10^{9}$ K km s$^{-1}$ pc$^2$, respectively. The northern companion is associated with a pair of merging cluster galaxies, while the southern one shows a southern tail in CO(4$\rightarrow$3), which was also detected in continuum, and we suggest it to be the most distant jellyfish galaxy for which ram pressure stripping is effectively able to strip off its dense molecular gas. This study probes the presence of rare gas-rich systems in the very central region of a distant cluster core, which will potentially merge into the BCG itself. Currently, we may thus be seeing the reversal of the star formation versus density relation at play in the distant universe. This is the first time the assembly of high-$z$ progenitors of our local BCGs can be studied in such great detail.