CF2057B Gorilla and the Exam

Due to a shortage of teachers in the senior class of the "T-generation", it was decided to have a huge male gorilla conduct exams for the students. However, it is not that simple; to prove his competence, he needs to solve the following problem. For an array $ b $ , we define the function $ f(b) $ as the smallest number of the following operations required to make the array $ b $ empty: - take two integers $ l $ and $ r $ , such that $ l \le r $ , and let $ x $ be the $ \min(b_l, b_{l+1}, \ldots, b_r) $ ; then - remove all such $ b_i $ that $ l \le i \le r $ and $ b_i = x $ from the array, the deleted elements are removed, the indices are renumerated. You are given an array $ a $ of length $ n $ and an integer $ k $ . No more than $ k $ times, you can choose any index $ i $ ( $ 1 \le i \le n $ ) and any integer $ p $ , and replace $ a_i $ with $ p $ . Help the gorilla to determine the smallest value of $ f(a) $ that can be achieved after such replacements.

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The description of the test cases follows. The first line of each set of input data contains two integers $ n $ and $ k $ ( $ 1 \le n \le 10^5 $ , $ 0 \le k \le n $ ) — the length of the array $ a $ and the maximum number of changes, respectively. The second line of each set of input data contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the array $ a $ itself. It is guaranteed that the sum of the values of $ n $ across all sets of input data does not exceed $ 10^5 $ .

For each set of input data, output a single integer on a separate line — the smallest possible value of $ f(a) $ .

In the first set of input data, $ f([48\,843]) = 1 $ , since the array consists of a single number, and thus it can be removed in one operation. In the second set of input data, you can change the second number to $ 2 $ , resulting in the array $ [2, 2, 2] $ , where $ f([2, 2, 2]) = 1 $ , since you can take the entire array as a subarray, the minimum on it is $ 2 $ , so we will remove all the $ 2 $ s from the array, and the array will become empty.