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: Wrong Answer)



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

int main(void) {
   
   int N,K;
   
   scanf("%d%d",&N,&K);
   
  // N = 5;
   //K = 1;
   char *S = malloc(sizeof(char)*N);
   
   scanf("%s",S);
   
   
   //strcpy(S,"00010");
   
   int *Kireme = malloc(sizeof(int)*(N+2));
   int *Fugou  = malloc(sizeof(int)*(N+2));
   int i;
   
   for(i = 0;i < N+2;i++){
      Kireme[i] = 0;
      Fugou[i] = 0;
   }
   
   int count1 = 0;
   int count2 = 0;
   int hanten = 0;
   for(i = 0;i < N - 1;i++){
      if(S[i] != S[i+1]){
         count1++;
         Kireme[count2] = count1;
         if(S[i] == '0'){
            Fugou[count2] = 0;
            hanten++;
         }
         else {
            Fugou[count2] = 1;
         }
         count1 = 0;
         count2++;
      }
      else {
         count1++;
      }
   }
   
   count1++;
   Kireme[count2] = count1;
   if(S[N-1] == '0'){
      Fugou[count2] = 0;
      hanten++;
   }
   else {
      Fugou[count2] = 1;
   }
   count2++;
   
   int kireme_num = count2;
   
   /*
   for(i = 0;i < kireme_num;i++){
      printf("%d %d %d\n",i,Kireme[i],Fugou[i]);
   }
   printf("%d\n",hanten);
   */
   
   int sousa;
   if(hanten > K){
      sousa = K;
   }
   else {
      printf("%d\n",N);
      return 0;
   }
   
   int j;
   int ans_num;
   int *Ans = malloc(sizeof(int)*kireme_num);
   for(i = 0;i < kireme_num;i++){
      Ans[i] = 0;
   }
   
   if(S[0] == '0'){
      for(i = 0;i < 2*sousa;i++){
         Ans[0] = Ans[0] + Kireme[i];
      }
      ans_num = hanten - K + 1;
      for(i = 1;i < ans_num;i++){
         if(i == 1){
            Ans[i] = Ans[i-1] - Kireme[0] - Kireme[(i-1)*2+1] + Kireme[(i+1)*2+0] + Kireme[(i+1)*2+1];
         }
         else {
            Ans[i] = Ans[i-1] - Kireme[(i-1)*2] - Kireme[(i-1)*2+1] + Kireme[(i+1)*2+0] + Kireme[(i+1)*2+1];
         }
      }
   }
   else {
      for(i = 0;i < 2*sousa+1;i++){
         Ans[0] = Ans[0] + Kireme[i];
      }
      ans_num = hanten - K + 1;
      
      for(i = 1;i < ans_num;i++){
         Ans[i] = Ans[i-1] - Kireme[(i-1)*2+1] - Kireme[(i-1)*2] + Kireme[(i+1)*2+1] + Kireme[(i+1)*2+2];
      }
   }
   
   int ans = 0;
   
   /*
   for(i = 0; i < ans_num;i++){
      printf("%d %d\n",i,Ans[i]);
   }
    */
   for(i = 0;i < ans_num;i++){
      if(ans <= Ans[i]){
         ans = Ans[i];
      }
   }
   
   printf("%d\n",ans);
   
   
   return 0;
}