A965. Redistricting--Platinum

The cow mega-city Bovinopolis is redistricting! -- always a contentious
political process between the two major cow breeds (Holsteins and Guernseys)
living there, since both breeds want to make sure they retain sufficient
influence in the Bovinopolis government.
The greater metropolitan area of Bovinopolis consists of a line of $N$
pastures ($1 \leq N \leq 3 \cdot 10^5$), each containing a single cow, which
is either a Holstein or a Guernsey.
The government of Bovinopolis wants to divide the greater metropolitan area
into some number of contiguous districts, so that each district contains at
most $K$ pastures ($1 \leq K \leq N$), and every pasture is contained in
exactly one district. Since the government is currently controlled by
Holsteins, they want to find a way to redistrict which minimizes the number of
Guernsey-majority or tied districts (a district is tied if the number of
Guernseys equals the number of Holsteins).
A concerned coalition of Guernseys is trying to figure out how much damage
might be done by the government's redistricting. Help them figure out the
worst-case minimum number of districts which are either Guernsey-majority or
tied.

The first line contains a two space-separated integers $N$ and $K$. The second
line contains a string of length $N$. Each character is either 'H' or 'G', for
Holstein or Guernsey.

Please output the minimum possible number of districts that are Guernsey-
majority or tied.