An edge colouring of $K_n$ with $k$ colours is a Gallai $k$-colouring if it does not contain any rainbow triangle. Gyárfás, Pálvölgyi, Patkós and Wales proved that there exists a number $g(k)$ such that $n\geq g(k)$ if and only if for any colour distribution sequence $(e_1,\cdots,e_k)$ with $\sum_{i=1}^ke_i=\binom{n}{2}$, there exist a Gallai $k$-colouring of $K_n$ with $e_i$ edges having colour $i$. They also showed that $Ω(k)=g(k)=O(k^2)$ and posed the problem of determining the exact order of magnitude of $g(k)$. Feffer, Fu and Yan improved both bounds significantly by proving $Ω(k^{1.5}/\log k)=g(k)=O(k^{1.5})$. We resolve this problem by showing $g(k)=Θ(k^{1.5}/(\log k)^{0.5})$.