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: Wrong Answer)

/*
    1) Notice the range of data;
    2) while(scanf) format need to init;
    3) Enough maxn;
    4) delete the freopen;
    5) remember to read this before submit;
*/
#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
int gcd(int a,int b){if (b == 0) return a; return gcd(b , a%b);}
int lcm(int a, int b){ return a/gcd(a,b)*b;}
inline int read(){
    int f = 1, x = 0;char ch = getchar();
    while (ch > '9' || ch < '0'){if (ch == '-')f = -f;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x * 10 + ch - '0';ch = getchar();}
    return x * f;
}
const int maxn = 1e5 + 10;
int all[maxn],tot = 0;
int iszero[maxn];
int main(){
    int n = read(),k = read();
    string s;
    cin >> s;
    int p = 0;
    while(p < s.length()){
        int cnt1 = 0,cnt2 = 0;
        while(s[p] == '1' && p < s.length()) {p++; cnt1++;}
        while(s[p] == '0' && p < s.length()) {p++; cnt2++;}
        if (cnt1 != 0){
            all[tot++] = cnt1; iszero[tot-1] = 0;
        }
        if (cnt2 != 0){
            all[tot++] = cnt2; iszero[tot-1] = 1;
        }
    }
    for(int i=0; i<tot; i++){
        if (iszero[i]){
            //cout << all[i] << ' ' << i << endl;
        }
    }
    int cnt = 0,sum = 0;
    for(int i=0; i<tot; i++){
        if (cnt == k) {
            if (i+1 == tot){
                cnt = i;
            }else{
                if (k != 0){
                    sum += all[i+1];
                    cnt = i+1;
                }else{
                    sum += all[i];
                    cnt = i;
                }
            }
            break;
        }else{
            sum += all[i];
            if (iszero[i]) cnt++;
        }
    }
    int l = 0,r = l+cnt,ans = sum;
    if (k != 0) r--;
    p = 0;
    //cout << l <<  ' ' <<  r << endl;
    while(r < tot){
        while(!iszero[l] && l < tot){
            sum -= all[l];
            l++;
        }
        if (l != tot)sum -= all[l++];
        while(!iszero[r] && r < tot){
            sum += all[r+1];
            r++;
        }
        sum += all[r+1]; r++;
        ans = max(ans,sum);
    }
    cout << ans << endl;
    return 0;
}