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: Wrong Answer)

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (progn (ql:quickload '(:cl-debug-print :fiveam))
                 (shadow :run)
                 (use-package :fiveam)))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)

;; BEGIN_INSERTED_CONTENTS
(declaim (inline read-line-into))
(defun read-line-into (buffer-string &key (in *standard-input*) (terminate-char #\Space))
  (declare (simple-base-string buffer-string))
  (loop for c of-type base-char =
           #-swank (code-char (read-byte in nil #.(char-code #\Newline)))
           #+swank (read-char in nil #\Newline)
        for idx from 0
        until (char= c #\Newline)
        do (setf (schar buffer-string idx) c)
        finally (when (< idx (length buffer-string))
                  (setf (schar buffer-string idx) terminate-char))
                (return (values buffer-string idx))))

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(defmacro println (obj &optional (stream '*standard-output*))
  `(let ((*read-default-float-format* 'double-float))
     (prog1 (princ ,obj ,stream) (terpri ,stream))))

(defconstant +mod+ 1000000007)

;; Body

(defun main ()
  (let* ((n (read))
         (k (read))
         (string (make-string n :element-type 'base-char))
         (s (make-array n :element-type 'bit :initial-element 0))
         (cumul (make-array (1+ n) :fill-pointer 0 :initial-element 0 :element-type 'uint32)))
    (declare (uint31 n k))
    (read-line-into string)
    (dotimes (i n)
      (setf (aref s i) (- (char-code (aref string i)) 48)))
    (vector-push 0 cumul)
    (loop with base = 0
          with base-bit = (aref s 0)
          for i below n
          do (unless (= base-bit (aref s i))
               (vector-push (- i base) cumul)
               (setf base i
                     base-bit (aref s i)))
          finally (vector-push (- i base) cumul))
    (dotimes (i n)
      (incf (aref cumul (1+ i)) (aref cumul i)))
    (println
     (loop with width = (if (zerop (aref s 0))
                            (* 2 k)
                            (+ (* 2 k) 1))
           for l below (length cumul)
           for r = (min n (+ l width))
           maximize (- (aref cumul r) (aref cumul l))))))

#-swank(main)