Secret Mission

Chefland is a country with $N$ cities (numbered $1$ through $N$) connected by $M$ bidirectional roads. Chef is on a mission to spread a secret recipe of a Rogan Josh dish. Chef has a sequence $A_1, A_2, \ldots, A_K$ and he must visit cities in the following way: he starts in the city $A_1$, travels to the city $A_2$, then travels from there to the city $A_3$ and so on until he reaches the city $A_