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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.InputMismatchException;
import java.util.*;
import java.io.*;
import java.lang.*;
public class Main{
    public static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.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);
        }
    }
 
    static long gcd(long a, long b){
        if (a == 0)
            return b;  
        return gcd(b % a, a);  
    }
    static long lcm(long a, long b)  {
        return (a*b)/gcd(a, b);  
    }
    public static void sortbyColumn(int arr[][], int col) 
    { 
        
        Arrays.sort(arr, new Comparator<int[]>() { 
            
          @Override              
          
          public int compare(final int[] entry1,  
                             final int[] entry2) { 
  
            
            if (entry1[col] > entry2[col]) 
                return 1; 
            else
                return -1; 
          } 
        });  
    } 
    static long func(long a[],long size,int s){
        long max1=a[s];
        long maxc=a[s];
        for(int i=s+1;i<size;i++){
            maxc=Math.max(a[i],maxc+a[i]);
            max1=Math.max(maxc,max1);
        }
        return max1;
    }
    public static class Pair<U extends Comparable<U>, V extends Comparable<V>> implements Comparable<Pair<U, V>> {
        public U x;
        public V y;
    
        public Pair(U x, V y) {
            this.x = x;
            this.y = y;
        }
    
        public int hashCode() {
            return (x == null ? 0 : x.hashCode() * 31) + (y == null ? 0 : y.hashCode());
        }
    
        public boolean equals(Object o) {
            if (this == o)
                return true;
            if (o == null || getClass() != o.getClass())
                return false;
            Pair<U, V> p = (Pair<U, V>) o;
            return (x == null ? p.x == null : x.equals(p.x)) && (y == null ? p.y == null : y.equals(p.y));
        }
    
        public int compareTo(Pair<U, V> b) {
            int cmpU = x.compareTo(b.x);
            return cmpU != 0 ? cmpU : y.compareTo(b.y);
        }
    
        public String toString() {
            return String.format("(%s, %s)", x.toString(), y.toString());
        }
    
    }
    static class MultiSet<U extends Comparable<U>> {
        public int sz = 0;
        public TreeMap<U, Integer> t;
 
        public MultiSet() {
            t = new TreeMap<>();
        }
 
        public void add(U x) {
            t.put(x, t.getOrDefault(x, 0) + 1);
            sz++;
        }
 
        public void remove(U x) {
            if (t.get(x) == 1) t.remove(x);
            else t.put(x, t.get(x) - 1);
            sz--;
        }
 
    }
    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }
    //static LinkedList<Integer> li;
    //static LinkedList<Integer> ans;
    static int ans1=0,ans2=0;
    static long dist[];
    static int visited[];
    static ArrayList<Integer> adj[];
    static int dp[][][];
    static int R,G,B;
    
    
    public static void main(String args[]){
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter w = new PrintWriter(outputStream);
        int t,i,j;
        
        t=in.nextInt();
        //t=1;
        while(t-->0){
            int n=in.nextInt(),k=in.nextInt();
            int[] arr=new int[n];
            TreeSet<Integer> tr=new TreeSet<>();
            for(i=0;i<n;i++){
                arr[i]=in.nextInt();
                tr.add(arr[i]);
            }
            if(k==1&&tr.size()>1){
                w.println(-1);
                continue;
            }
            if(k>=tr.size()){
                w.println(1);
                continue;
            }
            int ans=tr.size()-k;
            int sum=(int)(Math.ceil((double)(ans)/(k-1)))+1;
            w.println(sum);
        }
        w.close();
    }
}