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: Runtime Error)

"use strict";
function Main(input) {
    let lines = input.split("\n");
    let nk = lines.shift().split(/\s/).map((v) => v - 0);
    let N = nk[0], K = nk[1];
    let S = lines.shift().split(/\s/)[0].split("").map((v) => v - 0);
    let n = 0, Z = [];
    let p, b = S[0];
    while (n < N) {
        for (p = n; p < N && S[p] == b; p++) { }
        if (p < N) {
            let l = p - n;
            Z.push({kind: b, pos: n, len: l});
            b = (b + 1) % 2;
        }
        n = p;
    }
    if (Z[0].kind == 0) Z.unshift({kind: 1, pos: 0, len: 0});
    let zs = Z.reduce((ac, v) => ac + (v.kind == 0 ? 1 : 0), 0);
    const f = (v) => {
        let result = Z[v].len;
        if (v > 0) result += Z[v - 1].len;
        if (v < Z.length - 1) result += Z[v + 1].len;
        return result;
    }
    let ans = 0;
    for (let n = 0; n <= K*2; n++) {
        ans += Z[n].len;
    }
    console.log(ans);
}
if (typeof window == "undefined") Main(require("fs").readFileSync("/dev/stdin", "utf8"));