Given a complete graph $K_n$, and if we know there are $t$ $K_s$ ($s\ge 2$) in it, what can we say about the possible number $a$ of vertices and the number $b$ edges to form these $t$ cliques? We can assume $n\gg 1$ and $t(n)\gg 1$. So any asymptotical bounds would be helpful.

(There was a typo, $k(n)$ should be $t(n)$.)

For example, if all these $t$ cliques are vertex-disjoint, then $a=st$ and $b=\binom{s}{2}t$. If all of these $t$ cliques come from a larger clique, then $t\approx\binom{a}{s}$ and $b=\binom{a}{2}$. But what can we say about other cases? Do we have some relations between $a$, $b$, and $t$?