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)

N,K=map(int,input().split())
S=input()
N=int(len(S))
s=list(S)
c=[]
sum=0
cnt1=0
cnt0=0
if s[0]=="0":
  d=K*2
else:
  d=K*2+1
for i in range(N):
  if s[i]=="1":
    if cnt0!=0:
      c.append(cnt0)
    cnt1=cnt1+1
    cnt0=0
  else:
    if cnt1!=0:
      c.append(cnt1)
    cnt0=cnt0+1
    cnt1=0
if cnt0!=0:
  c.append(cnt0)
if cnt1!=0:
  c.append(cnt1)
C=int(len(c))
for i in range(d):
  sum=sum+c[i]
big=sum
for i in range(C-d):
  sum=sum+c[i+d]-c[i]
  if big<=sum:
    big=sum
print(big)