Maximum Subarray Sum with At Most K Distinct Elements

You are given an array of integers and an integer k. Your task is to find the maximum possible sum of any non-empty contiguous subarray that contains at most k distinct elements.

If the array is empty, output -inf (representing negative infinity).

The subarray must be contiguous and non-empty. Formally, given an array \(A = [a_1,a_2,\dots,a_n]\) and an integer \(k\), find the maximum sum of a subarray \(A[i..j]\) such that the number of distinct elements in \(A[i..j]\) is at most \(k\).

Note: In cases where the input array is empty, the answer is defined to be \(-\infty\), which should be printed as -inf.

inputFormat

The input is read from stdin and consists of:

1. A line containing two integers n and k, where n is the number of elements in the array and k is the maximum number of distinct elements allowed in the subarray.
2. If n > 0, a second line containing n integers separated by spaces representing the array elements. If n = 0, there is no array element line.

You can assume that when n = 0, k will be 0.

outputFormat

Output a single line to stdout containing the maximum possible sum of a contiguous subarray that contains at most k distinct elements. If the array is empty, output -inf.

5 2
1 2 1 2 3

6