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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;


namespace ClassLibrary1
{
    public class ListNode
    {
        public int val;
        public ListNode next;
        public ListNode(int x) { val = x; }
    }



    class StringComparator2 : IComparer<string>
    {
        int IComparer<string>.Compare(string a, string b)
        {
            int length = Math.Min(a.Length, b.Length);
            //Console.WriteLine("Comparing with length {0}", length);
            for (int i = 0; i < length; i++)
            {
                if (a[i] < b[i])
                {
                    //Console.WriteLine("returning -1");
                    return -1;
                }
                else if (a[i] > b[i]) return 1;
            }
            if (a.Length < b.Length) return -1;
            if (a.Length > b.Length) return 1;

            //Console.WriteLine("Why are we at the end?");
            return 0;
        }


    }

    class StringComparator3 : IEqualityComparer<string>
    {
        public bool Equals(string b1, string b2)
        {
            return Compare(b1, b2) == 0;
        }

        public int GetHashCode(string bx)
        {
            return bx.GetHashCode();
        }

        int Compare(string a, string b)
        {
            int length = Math.Min(a.Length, b.Length);
            //Console.WriteLine("Comparing with length {0}", length);
            for (int i = 0; i < length; i++)
            {
                if (a[i] < b[i])
                {
                    //Console.WriteLine("returning -1");
                    return -1;
                }
                else if (a[i] > b[i]) return 1;
            }
            if (a.Length < b.Length) return -1;
            if (a.Length > b.Length) return 1;

            //Console.WriteLine("Why are we at the end?");
            return 0;
        }
    }

    public class PriorityQueue<T> where T : IComparable
    {
        private IComparer<T> _comparer = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority Queue with custom comparer
        /// </summary>
        public PriorityQueue(int maxSize, IComparer<T> comparer)
        {
            _heap = new T[maxSize];
            _comparer = comparer;
        }

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        private int Compare(T x, T y)
        {
            if (_comparer != null) return _comparer.Compare(x, y);
            return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }


    }

    public class Class1
    {
        //static Dictionary<Tuple<long, long>, long> dic = new Dictionary<Tuple<long, long>, long>();

        static long mod = 1000000007;
        static long[] factorial = new long[1000001];
        static long[] invFactorial = new long[1000001];

        private static void calcFanctorial(long N)
        {
            factorial[0] = 1;
            for (int i = 1; i < N + 1; i++)
            {
                factorial[i] = factorial[i - 1] * i;
                factorial[i] %= mod;
            }
            invFactorial[N] = inv(factorial[N]);
            for (int i = (int)N; i > 0; i--)
            {
                invFactorial[i - 1] = invFactorial[i] * i % mod;
            }

        }



        class Tree
        {
            public HashSet<long> conn = new HashSet<long>();
        }


        static long bin(long a, long x, long n)
        {
            long y = a;
            long res = 1;
            while (x > 0)
            {
                if (x % 2 == 1)
                {
                    res = res * y % n;
                }
                x /= 2;
                y = y * y % n;
            }
            return res;
        }

        int cmp(string a, string b)
        {
            for (var i = 0; i < Math.Min(a.Length, b.Length); i++)
                if (a[i] < b[i]) return -1;
                else if (a[i] > b[i]) return 1;
            if (a.Length == b.Length) return 0;
            if (a.Length > b.Length) return 1;
            else return -1;
        }

        private static long nCm(long n, long m)
        {
            if (n < m) return 0;
            if (m < 0) return 0;

            return (factorial[n] * invFactorial[m] % mod) * invFactorial[n - m] % mod;
        }

        private static long nCm2(long n, long m)
        {
            if (n < m) return 0;
            if (m < 0) return 0;

            long res = 1;
            for (long i = n; i > n - m; i--)
            {
                res *= i;
                res %= mod;
            }

            return res * invFactorial[m] % mod;
        }

        public static long pow(long a, long b, long mod)
        {
            a %= mod;

            if (b <= 0) return 1;
            var t = pow(a, b / 2, mod);
            if ((b & 1) == 0) return t * t % mod;
            return t * t % mod * a % mod;
        }

        public static long Lcm(long a, long b)
        {
            return a * b % mod * inv(Gcd(a, b)) % mod;
        }

        public static long Lcm(long[] a)
        {
            List<long> vect = new List<long>();
            long lcm = 1;
            for (int i = 0; i < a.Count(); i++)
            {
                var factor = a[i] / GcdVector(vect, a[i]);
                vect.Add(factor);
                lcm = lcm * factor % mod;
            }
            return lcm;
        }

        static long GcdVector(List<long> a, long b)
        {
            long ma = 1;
            for (int i = 0; i < a.Count; i++)
                ma = ma * a[i] % b;
            return Gcd(b, ma);
        }

        public static long Gcd(long a, long b)
        {
            if (a < b)
                // 引数を入替えて自分を呼び出す
                return Gcd(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }

        public static long pow(long a, long b) => pow(a, b, mod);
        public static long inv(long a) => pow(a, mod - 2);

        private static char[][] ReadCharMatrix(long h)
        {
            char[][] mtx = new char[h][];
            for (int i = 0; i < h; i++)
            {
                var s = ReadString();
                mtx[i] = s.ToCharArray();
            }
            return mtx;
        }

        private static int[][] CreateIntMatrix(long h, long w)
        {
            int[][] mtx = new int[h][];
            for (int i = 0; i < h; i++)
            {
                mtx[i] = new int[w];
            }
            return mtx;
        }


        private static string ReadString()
        {
            return Console.ReadLine();
        }
        private static string[] ReadStringArr()
        {
            return Console.ReadLine().Split(' ');
        }
        private static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }
        private static long[] ReadLongArr()
        {
            string[] s = ReadStringArr();
            long[] l = new long[s.Length];
            for (int i = 0; i < l.Length; i++)
            {
                l[i] = long.Parse(s[i]);
            }

            return l;
        }
        private static int[] ReadIntArr()
        {
            string[] s = ReadStringArr();
            int[] l = new int[s.Length];
            for (int i = 0; i < l.Length; i++)
            {
                l[i] = int.Parse(s[i]);
            }

            return l;
        }


        static void Main(string[] args)
        {

            var NM = ReadLongArr();
            var S = ReadString().ToCharArray();

            int[] AA = new int[NM[0]];
            int flip = 0;

            var tmp = S[0];
            var index = 0;
            for(int i=1; i<S.Length;i++)
            {
                var cur = S[i];
                if(tmp != cur)
                {
                    AA[flip] = i - index;
                    tmp = cur;
                    index = i;
                    flip++;
                }
            }
            if(flip <= 1)
            {
                Console.WriteLine(NM[0]);
                return;
            }

            if(S[S.Length-1] != S[S.Length - 2])
            {
                AA[flip] = 1;
                flip++;
            }else
            {
                AA[flip] = S.Length - index;
            }


            var sum = new long[flip+2];
            sum[0] = 0;
            sum[1] = AA[0];
            for(int i=2; i<flip+2; i++)
            {
                sum[i] = sum[i - 1] + AA[i-1];
//                Console.WriteLine(sum[i]);
            }

            long res = 0;

            if(2 * NM[1] >= flip)
            {
                Console.WriteLine(NM[0]);
                return;
            }

            long sumLength = NM[1] * 2;
            if (S[0] == S[S.Length - 1] && S[0] == '1') res = sum[sumLength];
            else res = sum[sumLength - 1];

            for (long i= sumLength; i<sum.Length; i++)
            {
                res = Math.Max(res, sum[i] - sum[i - sumLength]);
            }
            if (S[0] == S[S.Length - 1] && S[0] == '1')
                res = Math.Max(res, sum[sum.Length - 1] - sum[sum.Length - 1 - sumLength -1]);


            Console.WriteLine(res);
        }


    }

}