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.lengthCompiled with clang 11 using the latest C++ 17 standard.
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