Problem:
Score : 400 points

Problem Statement

N people are arranged in a row from left to right.

You are given a string S of length N consisting of 0 and 1, and a positive integer K.

The i-th person from the left is standing on feet if the i-th character of S is 0, and standing on hands if that character is 1.

You will give the following direction at most K times (possibly zero):

Direction: Choose integers l and r satisfying 1 \leq l \leq r \leq N, and flip the l-th, (l+1)-th, ..., and r-th persons. That is, for each i = l, l+1, ..., r, the i-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.

Find the maximum possible number of consecutive people standing on hands after at most K directions.

Constraints

N is an integer satisfying 1 \leq N \leq 10^5.

K is an integer satisfying 1 \leq K \leq 10^5.

The length of the string S is N.

Each character of the string S is 0 or 1.

Input

Input is given from Standard Input in the following format:

N K
S

Output

Print the maximum possible number of consecutive people standing on hands after at most K directions.

Sample Input 1

5 1
00010

Sample Output 1

4

We can have four consecutive people standing on hands, which is the maximum result, by giving the following direction:

Give the direction with l = 1, r = 3, which flips the first, second and third persons from the left.

Sample Input 2

14 2
11101010110011

Sample Output 2

8

Sample Input 3

1 1
1

Sample Output 3

1

No directions are necessary.

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Runtime Error)

(defun window-sumlist (list windowsize)
  (labels ((mappedreduce (function sequence)
             (if (= 1 (length sequence))
                 (list (elt sequence 0))
                 (let* ((n (elt sequence 0)))
                   (mapcar (lambda (x) (setf n (funcall function n x)))
                           (subseq sequence 1))))))
    (let* ((lst-k (cons 0 (cons (car list) (mappedreduce #'+ list)))))
      (loop :for k :in (subseq lst-k windowsize)
            :for l :in lst-k
            :collect (- k l)))))


(window-sumlist '(1 2 4 8 16) 3)

(defun compressor (list)
  (let* ((ret nil))
    (map 'nil (lambda (x)
                (if (and ret (equal x (caar ret)))
                    (incf (cdar ret))
                    (push (cons x 1) ret)))
         list)
    ret))
(let* ((n (read))
       (m (read))
       (lst (mapcar #'cdr (compressor (read-line)))))
  (princ (reduce #'max (window-sumlist lst (1+ (* 2 m))))))