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

Input

10 3
mumumumumu

Output

6

Explanation

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

Example 2

Input

8 1
monashuni

Output

8