CF1551E.Fixed Points

Consider a sequence of integers $a_1, a_2, \ldots, a_n$. In one move, you can select any element of the sequence and delete it. After an element is deleted, all elements to the right are shifted to the left by $1$ position, so there are no empty spaces in the sequence. So after you make a move, the sequence's length decreases by $1$. The indices of the elements after the move are recalculated.

E. g. let the sequence be $a=[3, 2, 2, 1, 5]$. Let's select the element $a_3=2$ in a move. Then after the move the sequence will be equal to $a=[3, 2, 1, 5]$, so the $3$-rd element of the new sequence will be $a_3=1$ and the $4$-th element will be $a_4=5$.

You are given a sequence $a_1, a_2, \ldots, a_n$ and a number $k$. You need to find the minimum number of moves you have to make so that in the resulting sequence there will be at least $k$ elements that are equal to their indices, i. e. the resulting sequence $b_1, b_2, \ldots, b_m$ will contain at least $k$ indices $i$ such that $b_i = i$.

考虑一个整数序列 $a_1, a_2, \ldots, a_n$。在一次操作中，你可以选择序列中的任意一个元素并将其删除。被删除元素右侧的所有元素将向左移动一位，从而保证序列中不存在空位。因此，每次操作后，序列长度减少 $1$，且各元素的下标将重新计算。

例如，设序列为 $a=[3, 2, 2, 1, 5]$。若在某次操作中选择删除第 $3$ 个元素 $a_3=2$，则操作后的序列为 $a=[3, 2, 1, 5]$，此时新序列中第 $3$ 个元素为 $a_3=1$，第 $4$ 个元素为 $a_4=5$。

给定一个序列 $a_1, a_2, \ldots, a_n$ 和一个整数 $k$，你需要求出最少需要多少次操作，使得操作后得到的序列中至少有 $k$ 个元素满足“元素值等于其下标”，即：设操作后得到的序列为 $b_1, b_2, \ldots, b_m$，则其中至少存在 $k$ 个下标 $i$，使得 $b_i = i$。

The first line contains one integer $t$ ($1 \le t \le 100$) — the number of test cases. Then $t$ test cases follow.

Each test case consists of two consecutive lines. The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 2000$). The second line contains a sequence of integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le n$). The numbers in the sequence are not necessarily different.

It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2000$.

第一行包含一个整数 $t$（$1 \le t \le 100$），表示测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例由连续的两行组成。第一行包含两个整数 $n$ 和 $k$（$1 \le k \le n \le 2000$）。第二行包含一个整数序列 $a_1, a_2, \ldots, a_n$（$1 \le a_i \le n$）。该序列中的数字不一定互不相同。

保证所有测试用例的 $n$ 之和不超过 $2000$。

For each test case output in a single line:

• $-1$ if there's no desired move sequence;
• otherwise, the integer $x$ ($0 \le x \le n$) — the minimum number of the moves to be made so that the resulting sequence will contain at least $k$ elements that are equal to their indices.

对于每个测试用例，在一行中输出：

• 若不存在满足要求的移动序列，则输出 $-1$；
• 否则，输出整数 $x$（$0 \le x \le n$）—— 使得最终序列中至少有 $k$ 个元素等于其下标所需的最少移动次数。

In the first test case the sequence doesn't satisfy the desired condition, but it can be provided by deleting the first element, hence the sequence will be $[1, 2, 3, 4, 5, 6]$ and $6$ elements will be equal to their indices.

In the second test case there are two ways to get the desired result in $2$ moves: the first one is to delete the $1$-st and the $3$-rd elements so that the sequence will be $[1, 2, 3]$ and have $3$ elements equal to their indices; the second way is to delete the $2$-nd and the $3$-rd elements to get the sequence $[5, 2, 3]$ with $2$ desired elements.

在第一个测试用例中，原序列不满足目标条件，但可以通过删除第一个元素使其满足条件，此时序列为 $[1, 2, 3, 4, 5, 6]$，其中有 $6$ 个元素的值等于其下标（即位置编号）。

在第二个测试用例中，存在两种方式在 $2$ 步操作内达成目标：第一种是删除第 $1$ 个和第 $3$ 个元素，使序列变为 $[1, 2, 3]$，其中 $3$ 个元素的值等于其下标；第二种是删除第 $2$ 个和第 $3$ 个元素，得到序列 $[5, 2, 3]$，其中 $2$ 个元素的值等于其下标。