Chefina and Dishes

There are $N$ chefs (numbered $1$ through $N$) and $M$ dishes (numbered $1$ through $M$). For each valid $i$, the $i$-th chef can cook dishes of exactly one type $F_i$. Also, each chef is a friend of $K$ different chefs. Whenever some chef cooks a dish, he asks all chefs who either are his friends or know how to cook this dish to evaluate the dish. No chef may evaluate his own dish. All the