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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <string.h>

static int K;
static int END;
int search(int t, int g, int *CNT) {
#if 0
  printf("%d-%d CNT: ", t, g);
  for(int i = 0; i < END; i++) {
    printf("%d ", CNT[i]);
  }
  printf("\n");
#endif  

  if(t == END || g == K) {
    int MAX = 0;
    for(int j = 0; j < END; j++) {
      if(MAX < CNT[j])
	MAX = CNT[j];
    }
    return MAX;
  }

  int Ret = 0;
  Ret = search(t+1, g+0, CNT);
  for(int j = 0; j < END; j++) {
    int newCNT[100000];
    memcpy(newCNT, CNT, sizeof(int)*END);
    if(newCNT[j] >= 0) continue;

    int lp = -1;
    for(int k = j-1; k >= 0; k--) {
      if(newCNT[k] != 0) {
	lp = k;
	break;
      }
    }
    int rp = -1;
    for(int k = j+1; k < END; k++) {
      if(newCNT[k] != 0) {
	rp = k;
	break;
      }
    }
    int Ones = 0;
    if(lp != -1) Ones += newCNT[lp];
    if(rp != -1) Ones += newCNT[rp];
    Ones -= newCNT[j];
    //printf("%d-%d: Ones=%d CNT[%d]=%d\n", t, j, Ones, j, newCNT[j]);

    newCNT[j] = Ones;
    if(lp != -1)
      newCNT[lp] = 0;
    if(rp != -1)
      newCNT[rp] = 0;
    int Ret1 = search(t+1, g+1, newCNT);
    if(Ret < Ret1) Ret = Ret1;
  }

  return Ret;
}

int main(void) {
  int N;
  scanf("%d %d", &N, &K);
  int CNT[100000];
  memset(CNT, 0, sizeof(int)*100000);

  char S, P;
  for(int i = 0; i < N; i++) {
    scanf(" %c", &S);
    if(i != 0 && S != P) END++;
    P = S;
    if(S == '0') {
      CNT[END]--;
    }  else {
      CNT[END]++;
    }
  }
  END++;

  int MAX = search(0, 0, CNT);
  printf("%d\n", MAX);
  return 0;
}