Welcome to the Penthouse trophy

[KashSenpai]

So i'm trying to prestige on BO2 and i'm not the person who always encounter enemies so i don't do as well as other players on modes such as Kill Confirmed, Demolition and Domination. So i have recently stuck to League games because if you win you get 10k xp and if you lose you get 7.5k xp which is quite a lot in comparison to normal public matches. But the trophy about prestiging says you must prestige by playing public matches. Does that mean every game you have played until lv 55 must be through public matches? Or can it be anything, be it league or normal public match but as soon as you close into lv 55/prestige you must play public matches only in order to get the trophy?