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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program main
  implicit none
  integer :: n, k, j, l=2, res=1
  integer :: i(1000000)
  character(100000) :: s

  read *, n, k
  read *, s
  i(:) = n + 1
  i(1) = 1

  do j = 2, n
    if (s(j:j) /= s(j-1:j-1)) then
      i(l) = j
      l = l + 1
    end if
  end do

  do j = 1, n-1
    if (i(j) > n) exit
    if (s(i(j):i(j)) == '0') res = max(res, i(j+2*k)-i(j))
    if (s(i(j):i(j)) == '1') res = max(res, i(j+2*k+1)-i(j))
  end do

  print '(i0)', res

end program