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 Python (3.4.3) (judge verdict: Runtime Error)

# -*- coding: utf-8 -*-

import sys
input = sys.stdin.readline

def io_generator():
	return input()

#+++++++++++++++++++

def main(io):
	n,k= map(int, io().split())
	s=[int(i) for i in io()[:n]]
	init=s[0]
	ll=[]
	m=0
	pre=init
	for c in s:
		if c == pre:
			m+=1
		else:
			ll.append(m)
			m=1
			pre=c
	ll.append(m)
	
	#print(ll)
	off= 1 if init==1 else 0
	if len(ll)<=2*k + off:
		return n
	pre=sum(ll[:2*k+off])
	rr_max=pre
	for i in range(len(ll)//2 - k):
		cc=pre - ll[2*i] - ll[2*i+1] + ll[2*(k+i)+off]+ll[2*(k+i)+1+off]
		rr_max = max(rr_max, cc)
		pre=cc
	return rr_max


#++++++++++++++++++++

if __name__ == "__main__":
	io= lambda : io_generator()
	print (main(io))