# Cool line

Cossack Vus considers a string to be cool if it satisfies the following conditions:

All characters at even indices are identical.

All characters at odd indices are identical.

For instance, the strings `'wow'`

and `'ftftf'`

are cool, whereas `'cabab'`

and `'abcd'`

are not.

Cossack Vus has a string $s$ of length $n$, composed of lowercase Latin letters. He can change up to $k$ characters in the string to create a cool substring of the maximum possible length. Your task is to determine this maximum length.

## Input

The first line contains two integers $n$ and $k$ ($1≤n≤5⋅10_{6}$, $0≤k≤5⋅10_{6}$) — the length of the string and the maximum number of characters Cossack Vus is allowed to change.

The second line contains the string $s$, which consists of $n$ lowercase Latin letters.

## Output

Output a single integer — the maximum length of a cool substring that Cossack Vus can achieve.

## Examples

## Scoring

($7$ points): $n≤100$;

($14$ points): $n≤3000$;

($33$ points): $n≤100000$;

($23$ points): $k=0$;

($23$ points): no additional constraints.