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: Accepted)

"use strict";

function _toConsumableArray(arr) { return _arrayWithoutHoles(arr) || _iterableToArray(arr) || _nonIterableSpread(); }

function _nonIterableSpread() { throw new TypeError("Invalid attempt to spread non-iterable instance"); }

function _arrayWithoutHoles(arr) { if (Array.isArray(arr)) { for (var i = 0, arr2 = new Array(arr.length); i < arr.length; i++) { arr2[i] = arr[i]; } return arr2; } }

function _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError("Cannot call a class as a function"); } }

function _defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if ("value" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } }

function _createClass(Constructor, protoProps, staticProps) { if (protoProps) _defineProperties(Constructor.prototype, protoProps); if (staticProps) _defineProperties(Constructor, staticProps); return Constructor; }

function _toArray(arr) { return _arrayWithHoles(arr) || _iterableToArray(arr) || _nonIterableRest(); }

function _iterableToArray(iter) { if (Symbol.iterator in Object(iter) || Object.prototype.toString.call(iter) === "[object Arguments]") return Array.from(iter); }

function _slicedToArray(arr, i) { return _arrayWithHoles(arr) || _iterableToArrayLimit(arr, i) || _nonIterableRest(); }

function _nonIterableRest() { throw new TypeError("Invalid attempt to destructure non-iterable instance"); }

function _iterableToArrayLimit(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"] != null) _i["return"](); } finally { if (_d) throw _e; } } return _arr; }

function _arrayWithHoles(arr) { if (Array.isArray(arr)) return arr; }

function _main() {
  // ----------
  function splitNum(line) {
    return (Array.isArray(line) ? line : line.split(/\s+/)).map(function (n) {
      return parseInt(n);
    });
  }
  /**
   * Iterates over integers in [start, end).
   */


  /**
   * implementation of arbitrary-precision unsigned integer.
   */
  var Longer =
  /*#__PURE__*/
  function () {
    function Longer(value) {
      _classCallCheck(this, Longer);

      // enough for 64bit
      this.data = [0, 0, 0];
      var idx = 0;

      while (value !== 0) {
        this.data[idx] = value % Longer.border;
        value = Math.floor(value / Longer.border);
        idx++;
      }
    }

    _createClass(Longer, [{
      key: "add",
      value: function add(right) {
        var result = new Longer(0);
        var max = Math.max(this.data.length, right.data.length);
        var carry = 0;
        var idx = 0;

        for (; idx < max; idx++) {
          var sum = (this.data[idx] || 0) + (right.data[idx] || 0) + carry;
          result.data[idx] = sum % Longer.border;
          carry = Math.floor(sum / Longer.border);
        }

        if (carry > 0) {
          result.data[idx] = carry;
        }

        return result;
      }
    }, {
      key: "mul",
      value: function mul(right) {
        var result = new Longer(0);

        for (var lidx = 0; lidx < this.data.length; lidx++) {
          for (var ridx = 0; ridx < right.data.length; ridx++) {
            var me = this.data[lidx] * right.data[ridx];
            var tidx = lidx + ridx;
            var value = me;

            while (value > 0) {
              var sum = (result.data[tidx] || 0) + value;
              result.data[tidx] = sum % Longer.border;
              value = Math.floor(sum / Longer.border);
              tidx++;
            }
          }
        }

        return result;
      }
    }, {
      key: "toString",
      value: function toString() {
        var d = this.data.concat().reverse(); // let fsti = d.findIndex(v => v !== 0);

        var fsti = function (arr, pred) {
          for (var i = 0; i < arr.length; i++) {
            if (pred(arr[i], i)) {
              return i;
            }
          }

          return null;
        } // not full polyfill!
        (d, function (v) {
          return v !== 0;
        });

        if (fsti == null) {
          return "0";
        }

        return d.slice(fsti).map(function (v, i) {
          if (i === 0) {
            return String(v);
          } else {
            // return String(v).padStart(Longer.digits, "0");
            return padStart(String(v), Longer.digits, "0");
          }
        }).join("");

        function padStart(str, num, pad) {
          var n = num - str.length;
          var result = "";

          for (var i = 0; i < n; i++) {
            result += pad;
          }

          return result + str;
        }
      }
    }]);

    return Longer;
  }();
  /** digits per element. */


  Longer.digits = 7;
  Longer.border = Math.pow(10, Longer.digits);
  /**
   * UnionFind of integers in [0, N).
   * */

  /*#__PURE__*/
  (function () {
    function UnionFind(N) {
      _classCallCheck(this, UnionFind);

      this.nodes = new Array(N).fill(null).map(function () {
        return {
          parent: null,

          /**
           * size of set.
           * meaningless if not root
           */
          size: 1
        };
      });
    }
    /**
     * Find the root of element.
     */


    _createClass(UnionFind, [{
      key: "find",
      value: function find(elm) {
        var node = this.nodes[elm];
        var route = [];

        while (node.parent != null) {
          route.push(node);
          node = node.parent;
        }

        for (var _i2 = 0; _i2 < route.length; _i2++) {
          var r = route[_i2];
          r.parent = node;
        }

        return node;
      }
      /**
       * Union two sets.
       * @returns new root of merged set.
       */

    }, {
      key: "union",
      value: function union(elm1, elm2) {
        var node1 = this.find(elm1);
        var node2 = this.find(elm2);

        if (node1 === node2) {
          return;
        }

        node2.parent = node1;
        node1.size += node2.size;
        return node1;
      }
    }]);

    return UnionFind;
  })();
  /**
   * Runs a recursive function expressed as a generator function.
   */


  // ----------
  (function (input) {
    var lines = input.split("\n");

    var _splitNum = splitNum(lines[0]),
        _splitNum2 = _slicedToArray(_splitNum, 2),
        N = _splitNum2[0],
        K = _splitNum2[1];

    var S = lines[1].slice(0, N);

    var _count = function () {
      var ones = [];
      var zeroes = [];
      var cur = 1;
      var num = 0;
      var _iteratorNormalCompletion = true;
      var _didIteratorError = false;
      var _iteratorError = undefined;

      try {
        for (var _iterator = S[Symbol.iterator](), _step; !(_iteratorNormalCompletion = (_step = _iterator.next()).done); _iteratorNormalCompletion = true) {
          var c = _step.value;

          if (c === String(cur)) {
            num++;
          } else {
            (cur === 1 ? ones : zeroes).push(num);
            num = 1;
            cur ^= 1;
          }
        }
      } catch (err) {
        _didIteratorError = true;
        _iteratorError = err;
      } finally {
        try {
          if (!_iteratorNormalCompletion && _iterator.return != null) {
            _iterator.return();
          }
        } finally {
          if (_didIteratorError) {
            throw _iteratorError;
          }
        }
      }

      (cur === 1 ? ones : zeroes).push(num);
      cur ^= 1;

      if (cur === 1) {
        ones.push(0);
      }

      return {
        ones,
        zeroes
      };
    }(),
        ones = _count.ones,
        zeroes = _count.zeroes;

    if (zeroes.length <= K) {
      console.log(N);
      return;
    }

    var acc = ones.slice(0, K + 1).concat(zeroes.slice(0, K)).reduce(function (a, b) {
      return a + b;
    }, 0);
    var max = acc;

    for (var i = K; i < zeroes.length; i++) {
      acc = acc + ones[i + 1] - ones[i - K] + zeroes[i] - zeroes[i - K];

      if (max < acc) {
        max = acc;
      }
    }

    console.log(max);
  })(require("fs").readFileSync("/dev/stdin", "utf8"));
}

_main();