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.

Input

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 $10^5$.

Output

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

Note

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.

Samples

6
1 0
48843
3 1
2 3 2
5 3
1 2 3 4 5
7 0
4 7 1 3 2 4 1
11 4
3 2 1 4 4 3 4 2 1 3 3
5 5
1 2 3 4 5

1
1
2
5
2
1