Coins

Joe claims that he has telekinetic powers. This shocked Stan, a committed rationalist, who immediately asked Joe to prove it.

Joe decided to demonstrate his ability by tossing a coin. He says he can toss it so that heads come up exactly $k$ times as often as tails. Stan wrote down the result of every toss in order, and now he wants to find the longest run of consecutive tosses in which the number of heads is exactly $k$ times the number of tails.

The first line contains two integers $n$ and $k$ ($3 \le n \le 10^6$, $2 \le k \le n - 1$). Here $n$ is the number of tosses Joe made, and $k$ has the meaning described above.

The second line contains a string of $n$ characters describing the outcome of each toss. Each character is either O for heads or R for tails.

Print a single integer: the length of the longest run of consecutive tosses in which heads occur exactly $k$ times as often as tails. If no such run exists, print $0$.

In the sample input, the tosses from position 5 through 12 and from position 6 through 13 each contain exactly 6 heads and 2 tails, that is, three times as many heads as tails. No longer consecutive run has this property, so the answer is 8.