E. Fixed Pointstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputConsider 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.InputThe 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.OutputFor 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. ExampleInput
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
Output
1
2
-1
2
NoteIn 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.
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

1 2 -1 2 
['binary search', 'brute force', 'dp', '*2000']