## Is it NP-complete to test if a graph contains \$t\$ \$k\$-cliques?

Let $$(G,t,k)$$ – a graph with $$t$$ cliques with $$k$$ vertices (there are $$t$$ cliques of size $$k$$ in graph $$G$$), for $$t,k > 100$$. How to prove that $$(G,t,k)$$ is NP-complete?

It is obvious that it is in NP. I have tried to prove that $$k$$-CLIQUE language $$(G,k)$$ is reducible to a $$(G,t,k)$$ language. But I can’t get the idea, how to get $$t$$ of $$k$$-CLIQUES.