Petrol stations P40710

A car driver needs to plan a journey following a highway. With the tank full he can drive for at most $x$ kms. Knowing the location of the $n$ petrol stations on the road, which is the minimum number of refill stops necessary to travel for at least $D$ kms? Assume that, initially, the tank of the car is full of gasoline.

Input

Input is all natural numbers, and consists of several cases. Every case begins with $x$ and $D$, followed by $n$, followed by the distances in kms from the departure point to each petrol station. Assume $x > 0$, $D > 0$, $n \le 10^5$, and that all the given distances are different and between 1 and $D-1$. For all the given cases, it is always possible to reach the km $D$.

Output

For every case, print the minimum number of stops to travel for at least $D$ kms.