Regarding Nicca and Anicca natures of Avidya and Prajna

If Tanha (Craving) is caused by Avidya (Ignorance), and Avidya is originated and sustained by Tanha, then the origination of Avidya is part of a recursive cycle with no beginning. Yet Prajna (Wisdom) (as delivered through the Dharma) is purported to extinguish Avidya (Nirodha - Cessation). How can something with no beginning (cycle of dependent origination) have an end (Nirodha)? And likewise how can a state with no end (Nirvana) have a beginning (Nirodha)? Are Avidya and Nirvana therefore Nicca (Permanent and Unconditioned) or Anicca (Impermanent and Conditioned)? Put another away, if Prajna is Nicca, how could it give way to the origination and sustenance of Avidya in the first place? If Prajna is Anicca and has a beginning, then how can we say that Nirvana (which requires Prajna) is Nicca?