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 JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'

let S;

function myShift(i){
    let c=S[i];
    let count=0;
    let l = S.length;
    while(c===S[i] && i<l){
        count++;
        i++;
    }
    return count;
}

function Main(input) {
    let temp = input.trim().split('\n');
    let N = parseInt(temp[0].split(' ')[0]);
    let K = parseInt(temp[0].split(' ')[1]);
    S = temp[1];
    
    //console.log(N,K,S);
    let i=0;
    let count;
    let que=[];
    let sum=0;
    let max=0;
    let obj = {};

    if(N<=K){
        console.log(N);
        return;
    }

    //先頭が'1'だったらqueにいれておく。合計も足しておく
    if(S[0]==='1'){
        count = myShift(0);
        que.push({type:'1',count:count});
        sum += count;
        i += count;
        max = count;
        //console.log('start1:',count);
    }


    //足せるところまで0と次の1を足す。
    while(i<N){
        if(S[i]==='0'){
            K--;
            if(K<0){
                obj = que.shift();
                sum -= obj.count;
                K++;
                if(obj.type==='1'){
                    obj = que.shift();
                    sum -= obj.count;
                }
            }
        }
        //次を足す
        count = myShift(i);
        que.push({type:S[i],count:count});
        sum += count;
        i += count;
        max = Math.max(sum,max);
        //console.log('[',S[i-count],']','count:',count,' sum:',sum,' i:',i,' K:',K,' max:',max,' que:',que);
    }        

    console.log(max);

}
//*この行以降は編集しないでください（標準入出力から一度に読み込み、Mainを呼び出します）
Main(require("fs").readFileSync("/dev/stdin", "utf8"));