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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <vector>
#include <queue>
#include <string>
#include <cmath>
#include <algorithm>

using namespace std;

#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define BIT(X, i) ((X>>i)&1)
#define REP(i, a, b) for(int i = (a); i < (b); ++i)
#define rep(i, n) for(int i = 0; i < (n); ++i)
#define all(a) (a).begin(), (a).end()
#define r_all(a) (a).rbegin() (a).rend()

typedef long long ll;
typedef vector<ll> vi;
typedef vector<vi> vvi;
typedef pair<ll, ll> pii;
typedef vector<pii> vii;
typedef priority_queue<ll> pq;

const int MOD = 1e9+7;
const int INF = (1<<30);
const ll INFL = (1L<<62);

int main() {
  int n, k; cin >> n >> k;
  string s; cin >> s;
  int ans = 1;
  int l = 0, r = 0, cnt = 0;
  while (r < n) {
    if (s[r] == '0') {
      while (s[r] == '0') r++;
      cnt++;
    }
    while (s[r] == '1') r++;

    if (cnt <= k) {
      // cout << l << ", " << r << endl;
      ans = max(ans, r - l);
    }
    if (cnt == k) {
      while (s[l] == '1') l++;
      while (s[l] == '0') l++;
      cnt--;
    }
  }
  if (cnt == k) {
    // cout << l << ", " << r << endl;
    ans = max(ans, r - l);
  }

  cout << ans << endl;
  return 0;
}