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: Wrong Answer)

program main
Implicit None
	integer(8)::n,k,i,p,q,a
	integer(8),allocatable::t(:),u(:)
	character(len=100000)::s
	
	read*,n,k
	read*,s
	
	p=1
	if(s(1:1) == "0")then
		p=p+1
	endif
	
	
	do i = 2,n
		if(s(i:i) /= s(i-1:i-1)) p = p+1
	enddo
	
	a = p
	
	allocate(t(p),u(a))
	
	p = 1
	q = 1
	if(s(1:1) == "0")then
		t(1) = 0
		q = q+1
	endif
	
	do i = 2,n
		if(s(i:i) == s(i-1:i-1))then
			p = p+1
			else
			t(q) = p
			p = 1
			q = q+1
		endif
	enddo
	t(q) = p
	
	do i =2,a
		t(i) = t(i-1)+t(i)
	enddo
	
	k = 2*k+1
	
	if(a < k)then
		print"(i0)",n
		stop
	endif
	
	p = t(k)
	do i = 3,a-k+1,2
		if(p < t(k+i-1)-t(i-1)) p = t(k+i-1)-t(i-1)
	enddo
	
	print"(i0)",p
end program main