Make K-Subarray Sums Equal
<p>You are given a <strong>0-indexed</strong> integer array <code>arr</code> and an integer <code>k</code>. The array <code>arr</code> is circular. In other words, the first element of the array is the next element of the last element, and the last element of the array is the previous element of the first element.</p>

<p>You can do the following operation any number of times:</p>

<ul>
	<li>Pick any element from <code>arr</code> and increase or decrease it by <code>1</code>.</li>
</ul>

<p>Return <em>the minimum number of operations such that the sum of each <strong>subarray</strong> of length </em><code>k</code><em> is equal</em>.</p>

<p>A <strong>subarray</strong> is a contiguous part of the array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [1,4,1,3], k = 2
<strong>Output:</strong> 1
<strong>Explanation:</strong> we can do one operation on index 1 to make its value equal to 3.
The array after the operation is [1,3,1,3]
- Subarray starts at index 0 is [1, 3], and its sum is 4 
- Subarray starts at index 1 is [3, 1], and its sum is 4 
- Subarray starts at index 2 is [1, 3], and its sum is 4 
- Subarray starts at index 3 is [3, 1], and its sum is 4 
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [2,5,5,7], k = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong> we can do three operations on index 0 to make its value equal to 5 and two operations on index 3 to make its value equal to 5.
The array after the operations is [5,5,5,5]
- Subarray starts at index 0 is [5, 5, 5], and its sum is 15
- Subarray starts at index 1 is [5, 5, 5], and its sum is 15
- Subarray starts at index 2 is [5, 5, 5], and its sum is 15
- Subarray starts at index 3 is [5, 5, 5], and its sum is 15 
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arr[i] &lt;= 10<sup>9</sup></code></li>
</ul>

['rotate-array']
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    long long makeSubKSumEqual(vector<int>& arr, int k) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public long makeSubKSumEqual(int[] arr, int k) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def makeSubKSumEqual(self, arr, k):\n        \"\"\"\n        :type arr: List[int]\n        :type k: int\n        :rtype: int\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def makeSubKSumEqual(self, arr: List[int], k: int) -> int:\n        "}, {"value": "c", "text": "C", "defaultCode": "long long makeSubKSumEqual(int* arr, int arrSize, int k) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public long MakeSubKSumEqual(int[] arr, int k) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number[]} arr\n * @param {number} k\n * @return {number}\n */\nvar makeSubKSumEqual = function(arr, k) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function makeSubKSumEqual(arr: number[], k: number): number {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer[] $arr\n     * @param Integer $k\n     * @return Integer\n     */\n    function makeSubKSumEqual($arr, $k) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func makeSubKSumEqual(_ arr: [Int], _ k: Int) -> Int {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun makeSubKSumEqual(arr: IntArray, k: Int): Long {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  int makeSubKSumEqual(List<int> arr, int k) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func makeSubKSumEqual(arr []int, k int) int64 {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer[]} arr\n# @param {Integer} k\n# @return {Integer}\ndef make_sub_k_sum_equal(arr, k)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def makeSubKSumEqual(arr: Array[Int], k: Int): Long = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn make_sub_k_sum_equal(arr: Vec<i32>, k: i32) -> i64 {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (make-sub-k-sum-equal arr k)\n  (-> (listof exact-integer?) exact-integer? exact-integer?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec make_sub_k_sum_equal(Arr :: [integer()], K :: integer()) -> integer().\nmake_sub_k_sum_equal(Arr, K) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec make_sub_k_sum_equal(arr :: [integer], k :: integer) :: integer\n  def make_sub_k_sum_equal(arr, k) do\n    \n  end\nend"}]
{
  "name": "makeSubKSumEqual",
  "params": [
    {
      "name": "arr",
      "type": "integer[]"
    },
    {
      "type": "integer",
      "name": "k"
    }
  ],
  "return": {
    "type": "long"
  }
}
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Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. 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If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>"], "scala": ["Scala", "<p><code>Scala 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Array', 'Math', 'Greedy', 'Sorting', 'Number Theory']