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.*;
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //class  Declaration
 
static class pair implements Comparable < pair > {
    long x;
    long y;
    pair(long i, long j) {
        x = i;
        y = j;
    }
    public int compareTo(pair p) {
        if (this.x != p.x) {
            return Long.compare(this.x,p.x);
        } else {
            return Long.compare(this.y,p.y);
        }
    }
    public int hashCode() {
        return (x + " " + y).hashCode();
    }
    public String toString() {
        return x + " " + y;
    }
    public boolean equals(Object o) {
        pair x = (pair) o;
        return (x.x == this.x);
    }
}

// int[] dx = {0,0,1,-1};
// int[] dy = {1,-1,0,0};
// int[] ddx = {0,0,1,-1,1,-1,1,-1}; 
// int[] ddy = {1,-1,0,0,1,-1,-1,1};
 
final int inf = (int) 1e9 + 9;
final long biginf  = (long)1e18 + 7 ;
final long mod =  (long)1e9+7;  
//final long mod =  (long)998244353;  

void solve() throws Exception {
    int T=ni();
    while(T-->0){
        int n=ni(),k=ni();
        int[] arr= na(n);
        HashSet<Integer> hs= new HashSet<>();;
        for(int x: arr) hs.add(x);
        
        boolean pos = true ;
        int ans = 1;
        int req = hs.size() - k;
        k--;
        while(req > 0){
            if(k > 0){
                req -=k; 
            }
            else{
                pos = false ;
                break ;
            }
            ans++;
        } 
        pn(pos?ans:-1);
    }
    
        
}




long pow(long a, long b) {
    long result = 1;
    while (b > 0) {
        if (b % 2 == 1) result = (result * a) % mod;
        b /= 2;
        a = (a * a) % mod;
    }
    return result;
}
long gcd(long a, long b) {
    if (b == 0)
        return a;
    return gcd(b, a % b);
}
void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
 
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        //System.err.println(System.currentTimeMillis() - s + "ms");
}
public static void main(String[] args) throws Exception {
    //new Main().run();
    boolean memory = false ;
    if(memory) new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();System.exit(1);}}}, "1", 1 << 28).start();
    else new Main().run();
}
 
//output methods
private void dbg(Object... o){ System.err.println(Arrays.deepToString(o));}
void p(Object... o){for(Object oo:o)out.print(oo+" ");}
void pn(Object... o){for(int i = 0; i< o.length; i++)out.print(o[i]+(i+1 < o.length?" ":"\n"));}
void pni(Object... o){for(Object oo:o)out.print(oo+" ");out.println();out.flush();}
 
//input methods

private int[][] ng(int n, int e, int[] from, int[] to, boolean f){
    int[][] g = new int[n+1][];int[]cnt = new int[n+1];
    for(int i = 0; i< e; i++){
        cnt[from[i]]++;
        if(f)cnt[to[i]]++;
    }
    for(int i = 0; i<= n; i++)g[i] = new int[cnt[i]];
    for(int i = 0; i< e; i++){
        g[from[i]][--cnt[from[i]]] = to[i];
        if(f)g[to[i]][--cnt[to[i]]] = from[i];
    }
    return g;
}
private int[][][] nwg(int n, int e, int[] from, int[] to, boolean f){
    int[][][] g = new int[n+1][][];int[]cnt = new int[n+1];
    for(int i = 0; i< e; i++){
        cnt[from[i]]++;
        if(f)cnt[to[i]]++;
    }
    for(int i = 0; i<= n; i++)g[i] = new int[cnt[i]][];
    for(int i = 0; i< e; i++){
        g[from[i]][--cnt[from[i]]] = new int[]{to[i], i, 0};
        if(f) g[to[i]][--cnt[to[i]]] = new int[]{from[i], i, 1};
    }
    return g;
}


private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
 
 
private int readByte() {
    if (lenbuf == -1) throw new InputMismatchException();
    if (ptrbuf >= lenbuf) {
        ptrbuf = 0;
        try {
            lenbuf = is.read(inbuf);
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        if (lenbuf <= 0) return -1;
    }
    return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) {
    return !(c >= 33 && c <= 126);
}
private int skip() {
    int b;
    while ((b = readByte()) != -1 && isSpaceChar(b));
    return b;
}
 
private double nd() {
    return Double.parseDouble(ns());
}
private char nc() {
    return (char) skip();
}
 
private String ns() {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
        sb.appendCodePoint(b);
        b = readByte();
    }
    return sb.toString();
}
 
private char[] ns(int n) {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while (p < n && !(isSpaceChar(b))) {
        buf[p++] = (char) b;
        b = readByte();
    }
    return n == p ? buf : Arrays.copyOf(buf, p);
}
 
private char[][] nm(int n, int m) {
    char[][] map = new char[n][];
    for (int i = 0; i < n; i++) map[i] = ns(m);
    return map;
}
 
private int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++) a[i] = ni();
    return a;
}
 
private int ni() {
    int num = 0, b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private long nl() {
    long num = 0;
    int b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}

}