Handstand

AtCoder

IDabc124_d

Time2000ms

Memory256MB

Difficulty—

$N$ 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: $N$ $K$ $S$ [samples]

Samples

Input #1

5 1
00010

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.

Input #2

14 2
11101010110011

Output #2

Input #3

1 1
1

Output #3

1

No directions are necessary.

API Response (JSON)

{
  "problem": {
    "name": "Handstand",
    "description": {
      "content": "$N$ 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 fee",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc124_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ people are arranged in a row from left to right.\nYou are given a string $S$ of length $N$ consisting of `0` and `1`, and a positive integer $K$.\nThe $i$\\-th person from the left is standing on fee...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments