Consider a sequence of integers a_1, a_2, …, 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, …, 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, …, b_m will contain at least k indices i such that b_i = i.

Input

The first line contains one integer t (1 ≤ t ≤ 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 ≤ k ≤ n ≤ 2000). The second line contains a sequence of integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 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 ≤ x ≤ 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. 

Example

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


Output


1
2
-1
2

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.
import java.util.*;

public class main {
    public static final Scanner sc = new Scanner(System.in);

    public static int gcd(int a,int b) {
        return b==0?a:gcd(b, a%b);
    }
    public static int max(int a,int b) {
        if(a>b) return a;
        else return b;
    }


    public static void solve(){
        int n=sc.nextInt(),k=sc.nextInt();
        int[] a=new int[n+1],ans=new int[n+1];
        for(int i=1;i<=n;i++) a[i]=sc.nextInt();
        int mi=n+1;
        for(int i=1;i<=n;i++){
            ans[i]=-1000000000;
            if(a[i]>i) continue;
            ans[i]=1;
            for(int j=1;j<i;j++){
                if(a[i]>a[j]&&a[i]-a[j]<=i-j) ans[i]=max(ans[i],ans[j]+1);
            }
            if(ans[i]>=k&&i-a[i]<mi) mi=i-a[i];
        }
        if(mi!=n+1) System.out.println(mi);
        else System.out.println(-1);
    }
    public static void main(String[] args) {
        int T=1;
        T=sc.nextInt();
        while(--T>=0) solve();
    }
}
