Pair Count

We define the value of a string $T$ of length $m$ as the number of pairs $(i, j)$ such that $i < j$, $T_i$ is m, and $T_j$ is u.

Given a string $S$ of length $N$ and an integer $C$, find the maximum possible value of $X$ such that there exists a contiguous substring of $S$ with length $X$ and value at most $C$.

Input

The first line contains two integers $N$ and $C$.

The second line contains the string $S$ of length $N$.

Output

Print a single integer representing the maximum possible length $X$.

Constraints

• $1 \le N \le 10^6$
• $1 \le C \le 10^18$
• $S$ consists only of lowercase English letters.

Example 1

10 3
mumumumumu

6

Explanation

The longest substring of $S$ that has the value $\le 3$ is $umumum$.

Example 2

8 1
monashuni

8