a particular star from the BS can be found in the $k$-neighbourhood of several other stars, and we give it the contamination $p_{cont}$ of the neighbourhood with the highest $k$, where this star is found.

![image](Figure2a.pdf){width="\textwidth"}

![image](Figure2b.pdf){width="\textwidth"}

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In Fig. \[Figure1\] we show the distribution of all stars from the BS coded by their individual $p_{cont}$. The left panel shows the distribution in the $\Delta V_{\parallel}$, $\Delta V_{\bot}$-plane, in the right panel we present the same set of stars, but in the $X_P,Y_P$-plane. The background is filled by the vast majority (97.2%) of stars from the BS having $p_{cont}$ $\approx$ 1 (cases $k$ = 0,1,2 in Table \[table:1\]), which cover the whole area. Stars having intermediate contamination (cases $k$ = 3,4) are clearly identifiable by their colour, and the remaining stars with $p_{cont} \approx 0$ are shown in black. The huge signal centred at $\Delta V_{\parallel}$, $\Delta V_{\bot}$ = (0, 0) in the left panel and $X_P,Y_P$ = (0, 0) in the right panel represents Praesepe and its tails. A minor over-density at about $\Delta V_{\parallel}$, $\Delta V_{\bot}$ = (2.5, 6.3) and $X_P,Y_P$ = (445, 220) is the open cluster Collinder 350 and has nothing to do with Praesepe. In 