You are given a non-decreasing array of non-negative integers a_1, a_2, …, a_n. Also you are given a positive integer k.

You want to find m non-decreasing arrays of non-negative integers b_1, b_2, …, b_m, such that:

  * The size of b_i is equal to n for all 1 ≤ i ≤ m. 
  * For all 1 ≤ j ≤ n, a_j = b_{1, j} + b_{2, j} + … + b_{m, j}. In the other word, array a is the sum of arrays b_i. 
  * The number of different elements in the array b_i is at most k for all 1 ≤ i ≤ m. 



Find the minimum possible value of m, or report that there is no possible m.

Input

The first line contains one integer t (1 ≤ t ≤ 100): the number of test cases.

The first line of each test case contains two integers n, k (1 ≤ n ≤ 100, 1 ≤ k ≤ n).

The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_1 ≤ a_2 ≤ … ≤ a_n ≤ 100, a_n > 0).

Output

For each test case print a single integer: the minimum possible value of m. If there is no such m, print -1.

Example

Input


6
4 1
0 0 0 1
3 1
3 3 3
11 3
0 1 2 2 3 3 3 4 4 4 4
5 3
1 2 3 4 5
9 4
2 2 3 5 7 11 13 13 17
10 7
0 1 1 2 3 3 4 5 5 6


Output


-1
1
2
2
2
1

Note

In the first test case, there is no possible m, because all elements of all arrays should be equal to 0. But in this case, it is impossible to get a_4 = 1 as the sum of zeros.

In the second test case, we can take b_1 = [3, 3, 3]. 1 is the smallest possible value of m.

In the third test case, we can take b_1 = [0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2] and b_2 = [0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2]. It's easy to see, that a_i = b_{1, i} + b_{2, i} for all i and the number of different elements in b_1 and in b_2 is equal to 3 (so it is at most 3). It can be proven that 2 is the smallest possible value of m.
     import java.io.*;
    import java.util.*;
    import java.math.*;
    import java.lang.*;

    public class Main implements Runnable 
    {
        static class InputReader 
        {
            private InputStream stream;
            private byte[] buf = new byte[1024];
            private int curChar;
            private int numChars;
            private SpaceCharFilter filter;
            private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

            public InputReader(InputStream stream) 
            {
                this.stream = stream;
            }
            
            public int read()
            {
                if (numChars==-1) 
                    throw new InputMismatchException();
                
                if (curChar >= numChars) 
                {
                    curChar = 0;
                    try
                    {
                        numChars = stream.read(buf);
                    }
                    catch (IOException e)
                    {
                        throw new InputMismatchException();
                    }
                    
                    if(numChars <= 0)               
                        return -1;
                }
                return buf[curChar++];
            }
        
            public String nextLine()
            {
                String str = "";
                try
                {
                    str = br.readLine();
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }    
                return str;
            }
            public int nextInt() 
            {
                int c = read();
                
                while(isSpaceChar(c)) 
                    c = read();
            
                int sgn = 1;
            
                if (c == '-') 
                {
                    sgn = -1;
                    c = read();
                }
                
                int res = 0;
                do
                {
                    if(c<'0'||c>'9') 
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                while (!isSpaceChar(c)); 
            
                return res * sgn;
            }
            
            public long nextLong() 
            {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-')
                {
                    sgn = -1;
                    c = read();
                }
                long res = 0;
                
                do 
                {
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }    
                while (!isSpaceChar(c));
                    return res * sgn;
            }
            
            public double nextDouble() 
            {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                int sgn = 1;
                if (c == '-')
                {
                    sgn = -1;
                    c = read();
                }
                double res = 0;
                while (!isSpaceChar(c) && c != '.') 
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
                }
                if (c == '.') 
                {
                    c = read();
                    double m = 1;
                    while (!isSpaceChar(c))
                    {
                        if (c == 'e' || c == 'E')
                            return res * Math.pow(10, nextInt());
                        if (c < '0' || c > '9')
                            throw new InputMismatchException();
                        m /= 10;
                        res += (c - '0') * m;
                        c = read();
                    }
                }
                return res * sgn;
            }
        
            public String readString() 
            {
                int c = read();
                while (isSpaceChar(c))
                    c = read();
                StringBuilder res = new StringBuilder();
                do 
                {
                    res.appendCodePoint(c);
                    c = read();
                } 
                while (!isSpaceChar(c));
                
                return res.toString();
            }
        
            public boolean isSpaceChar(int c) 
            {
                if (filter != null)
                    return filter.isSpaceChar(c);
                return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
            }
        
            public String next()
            {
                return readString();
            }
            
            public interface SpaceCharFilter
            {
                public boolean isSpaceChar(int ch);
            }
        }
        public static void main(String args[]) throws Exception 
        {
            new Thread(null, new Main(),"Main",1<<27).start();
        }
        
        static class Pair{
            int f;
            int s;
            
            
            Pair(int f,int s){
                this.f=f;
                this.s=s;
                
            }
            
            public static Comparator<Pair> wc = new Comparator<Pair>(){
                public int compare(Pair e1,Pair e2){
                    
                    //reverse order
                    if(e1.s < e2.s) 
                        return 1;  // 1 for swaping.
                    else if (e1.s > e2.s) 
                        return -1; 
                    else {
                        //System.out.println("* "+e1.nod+" "+e2.nod);
                        return 0;
                    } 
                    
                }
            };	
        }

        public static long gcd(long a,long b){
            if(b==0)return a;
            else return gcd(b,a%b);
        }


        ////recursive BFS
        public static int bfsr(int s,ArrayList<Integer>[] a,boolean[] b,int[] pre){
            b[s]=true;
            int p = 1;
            int n = pre.length -1;
            int t = a[s].size();
            int max = 1;
            for(int i=0;i<t;i++){
                int x = a[s].get(i);
                if(!b[x]){
                    //dist[x] = dist[s] + 1;
                    int xz =  (bfsr(x,a,b,pre));
                    p+=xz;
                    max = Math.max(xz,max);
                }
            }
            max = Math.max(max,(n-p));
            pre[s] = max;
            return p;
        }

    //// iterative BFS
        public static int bfs(int s,ArrayList<Integer>[] a,int[] dist,boolean[] b,PrintWriter w){
            b[s]=true;
            int siz = 0;
            
            Queue<Integer> q = new LinkedList<>();
            q.add(s);
            while(q.size()!=0){
                int i=q.poll();
                Iterator<Integer> it = a[i].listIterator();
                int z=0;
                while(it.hasNext()){
                    z=it.next();
                    if(!b[z]){
                        b[z]=true;
                        dist[z] = dist[i] + 1;
                        siz++;
                        q.add(z);
                    }
                }   
            
            }
            return siz;
        }

        public static int lower(int key, int[] a){
            int l = 0;
            int r = a.length-1;
            int res = 0;

            while(l<=r){
                int mid = (l+r)/2;

                if(a[mid]<=key){
                    l = mid+1;
                    res = mid+1;
                }
                else{
                    r = mid -1;
                }
            }

            return res;
        }

        


    //////////////////////////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////////////


        public void run()
        {
            InputReader sc = new InputReader(System.in);
            PrintWriter w = new PrintWriter(System.out);
            long defaultValue=0;
            

            
            int tc = sc.nextInt();
            while(tc-->0){
                int n = sc.nextInt();
                int k = sc.nextInt();
                int[] a = new int[n];
                boolean[] b = new boolean[110]; 
                int x = 0;
                for(int i=0;i<n;i++){
                    a[i] = sc.nextInt();
                    if(!b[a[i]]){
                        x++;
                        b[a[i]] = true;
                    }
                }
                int ans = 1;
                if(k==1){
                    if(x>1)
                        ans = -1;
                    
                }
                else{
                    x-=k;
                    while(x>0){
                        ans++;
                        x-=(k-1);       
                    }
                    
                
                }
                
                w.println(ans);







            }
            w.flush();
            w.close();
        }
        
    
        

        
    }

