A14416 | 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 $b_i = i$ .

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 $2000$ .

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.