A Game of Thrones

There are $M$ kings numbered $1$ to $M$ in Easteros. There are $N$ thrones numbered $1$ to $N$. Initially, the first $N$ kings hold the $N$ thrones in any order (it is not necessary that throne $i$ has king $i$) Kings numbered $N+1$ to $M$ each choose a single throne and start attacking in order i.e King $N+1$ attacks a throne, then King $N+2$ (maybe a different throne) and so on till King $M$. E