Fixed Points

1000ms

262144K

Description:

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 $$$b_i = i$$$.

Input:

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 $$$2000$$$.

Output:

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.

Sample Input:

4
7 6
1 1 2 3 4 5 6
5 2
5 1 3 2 3
5 2
5 5 5 5 4
8 4
1 2 3 3 2 2 5 5

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1551E