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: Accepted)

n,k=map(int,input().split())
s=input()
s01=[[1,s[0]]]
for i in range(1,n):
  if s[i]==s[i-1]:
    s01[-1][0]+=1
  else:
    s01.append([1,s[i]])
a=len([i0 for i0,i1 in s01 if i1=='0'])
if a<=k:
  print(n)
  exit()
# 累計和
si=0
sums=[0]
for s01i in s01:
  si+=s01i[0]
  sums.append(si)
ans=0
#print(s01)
#print(sums)
l=0 if s[0]=='0' else 1
for i in range(l,len(s01),2):
  l=max(0,i-1)
  r=min(len(sums)-1,2*k+i)
  #print(sums[r]-sums[l],i,l,r)
  ans=max(ans,sums[r]-sums[l])
print(ans)