B. Ternary Nightmare
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Vitya woke up from his nightmare and turned on his laptop in yet another boring day as a mid-career software engineer. Then, in horror, he noticed that his computer has turned ternary — in addition to $$$0$$$ and $$$1$$$, he now notices $$$2$$$ in the data flow too. This is indeed worse than any nightmare he could have ever expected — essential programs he wrote were based on the seemingly unshakable assumption that binary "bits" would be received, not ternary "trits" (this is a real word: see the Wikipedia article).

Fortunately, Vitya built his programs with resilience in mind: within a data stream, it can withstand a certain number of unexpected values (in this case, '2'), $$$k$$$, before it starts behaving unpredictably. Since his laptop has just turned ternary, he needs your help finding the maximum length of the continuous sub-stream from his data stream of length $$$n$$$ that can be run through the programs without causing unexpected behavior.

Input

The first line consists of two integers, $$$n$$$ and $$$k\ (1\leq n \leq 10^5, 0\leq k \leq n)$$$ — the length of the data stream and the maximum allowed unexpected values.

The second line consists of a single string $$$s$$$, representing the ternary data stream, made up of exclusively $$$0$$$, $$$1$$$, and $$$2$$$.

Output

The length of the longest substring from the string representing the data stream containing at most $$$k$$$ instances of the value $$$2$$$, which is an unexpected value for Vitya's program.

Example
Input
16 3
1201012200120012
Output
13
Note

In the sample, the longest substring from the data flow can be highlighted as $$$12\textbf{0101220012001}2$$$.