You are given a 0-indexed array arr consisting of n positive integers, and a positive integer k.
The array arr is called K-increasing if arr[i-k] <= arr[i] holds for every index i, where k <= i <= n-1.
arr = [4, 1, 5, 2, 6, 2] is K-increasing for k = 2 because:\n\n\tarr[0] <= arr[2] (4 <= 5)arr[1] <= arr[3] (1 <= 2)arr[2] <= arr[4] (5 <= 6)arr[3] <= arr[5] (2 <= 2)arr is not K-increasing for k = 1 (because arr[0] > arr[1]) or k = 3 (because arr[0] > arr[3]).In one operation, you can choose an index i and change arr[i] into any positive integer.
Return the minimum number of operations required to make the array K-increasing for the given k.
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Example 1:
\n\n\nInput: arr = [5,4,3,2,1], k = 1\nOutput: 4\nExplanation:\nFor k = 1, the resultant array has to be non-decreasing.\nSome of the K-increasing arrays that can be formed are [5,6,7,8,9], [1,1,1,1,1], [2,2,3,4,4]. All of them require 4 operations.\nIt is suboptimal to change the array to, for example, [6,7,8,9,10] because it would take 5 operations.\nIt can be shown that we cannot make the array K-increasing in less than 4 operations.\n\n\n
Example 2:
\n\n\nInput: arr = [4,1,5,2,6,2], k = 2\nOutput: 0\nExplanation:\nThis is the same example as the one in the problem description.\nHere, for every index i where 2 <= i <= 5, arr[i-2] <= arr[i].\nSince the given array is already K-increasing, we do not need to perform any operations.\n\n
Example 3:
\n\n\nInput: arr = [4,1,5,2,6,2], k = 3\nOutput: 2\nExplanation:\nIndices 3 and 5 are the only ones not satisfying arr[i-3] <= arr[i] for 3 <= i <= 5.\nOne of the ways we can make the array K-increasing is by changing arr[3] to 4 and arr[5] to 5.\nThe array will now be [4,1,5,4,6,5].\nNote that there can be other ways to make the array K-increasing, but none of them require less than 2 operations.\n\n\n
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Constraints:
\n\n1 <= arr.length <= 1051 <= arr[i], k <= arr.length给你一个下标从 0 开始包含 n 个正整数的数组 arr ，和一个正整数 k 。
如果对于每个满足 k <= i <= n-1 的下标 i ，都有 arr[i-k] <= arr[i] ，那么我们称 arr 是 K 递增 的。
arr = [4, 1, 5, 2, 6, 2] 对于 k = 2 是 K 递增的，因为：\n\n\tarr[0] <= arr[2] (4 <= 5)arr[1] <= arr[3] (1 <= 2)arr[2] <= arr[4] (5 <= 6)arr[3] <= arr[5] (2 <= 2)arr 对于 k = 1 不是 K 递增的（因为 arr[0] > arr[1]），对于 k = 3 也不是 K 递增的（因为 arr[0] > arr[3] ）。每一次 操作 中，你可以选择一个下标 i 并将 arr[i] 改成任意 正整数。
请你返回对于给定的 k ，使数组变成 K 递增的 最少操作次数 。
\n\n
示例 1：
\n\n输入：arr = [5,4,3,2,1], k = 1\n输出：4\n解释：\n对于 k = 1 ，数组最终必须变成非递减的。\n可行的 K 递增结果数组为 [5,6,7,8,9]，[1,1,1,1,1]，[2,2,3,4,4] 。它们都需要 4 次操作。\n次优解是将数组变成比方说 [6,7,8,9,10] ，因为需要 5 次操作。\n显然我们无法使用少于 4 次操作将数组变成 K 递增的。\n\n\n
示例 2：
\n\n输入：arr = [4,1,5,2,6,2], k = 2\n输出：0\n解释：\n这是题目描述中的例子。\n对于每个满足 2 <= i <= 5 的下标 i ，有 arr[i-2] <= arr[i] 。\n由于给定数组已经是 K 递增的，我们不需要进行任何操作。\n\n
示例 3：
\n\n输入：arr = [4,1,5,2,6,2], k = 3\n输出：2\n解释：\n下标 3 和 5 是仅有的 3 <= i <= 5 且不满足 arr[i-3] <= arr[i] 的下标。\n将数组变成 K 递增的方法之一是将 arr[3] 变为 4 ，且将 arr[5] 变成 5 。\n数组变为 [4,1,5,4,6,5] 。\n可能有其他方法将数组变为 K 递增的，但没有任何一种方法需要的操作次数小于 2 次。\n\n\n
\n\n
提示：
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