Set C=4 sum_{j=0}^{k-2}(3M)^j, G=4 sum_{j=0}^{k-2}3^j, D=Cn and r=Gn/M. For M>=G, insertion bounds give depth at most D and at most floor(r) B choices. Deterministic branching identifies a node by its depth and B positions: at most (D+1) sum_{a=0}^{floor(r)} binom(D,a) descriptions. The factorial bound a!>=(a/e)^a gives binom(D,a)<=(eD/a)^a<=(eD/r)^r for 1<=a<=r<=D, because (eD/a)^a increases up to D. There are at most D+1 terms, including a=0. Since eD/r=eCM/G<=4CM, the tree has at most (Cn+1)^2 2^{(Gn/M)log2(4CM)} nodes. If r<1 no B choices are possible: at most D+1 nodes suffice.