You are given an array a[0 … n - 1] = [a_0, a_1, …, a_{n - 1}] of zeroes and ones only. Note that in this problem, unlike the others, the array indexes are numbered from zero, not from one.

In one step, the array a is replaced by another array of length n according to the following rules: 

  1. First, a new array a^{→ d} is defined as a cyclic shift of the array a to the right by d cells. The elements of this array can be defined as a^{→ d}_i = a_{(i + n - d) mod n}, where (i + n - d) mod n is the remainder of integer division of i + n - d by n. 

It means that the whole array a^{→ d} can be represented as a sequence $$$a^{→ d} = [a_{n - d}, a_{n - d + 1}, …, a_{n - 1}, a_0, a_1, …, a_{n - d - 1}]$$$

  2. Then each element of the array a_i is replaced by a_i  \&  a^{→ d}_i, where \& is a logical "AND" operator. 



For example, if a = [0, 0, 1, 1] and d = 1, then a^{→ d} = [1, 0, 0, 1] and the value of a after the first step will be [0  \&  1, 0  \&  0, 1  \&  0, 1  \&  1], that is [0, 0, 0, 1].

The process ends when the array stops changing. For a given array a, determine whether it will consist of only zeros at the end of the process. If yes, also find the number of steps the process will take before it finishes.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The next 2t lines contain descriptions of the test cases. 

The first line of each test case description contains two integers: n (1 ≤ n ≤ 10^6) — array size and d (1 ≤ d ≤ n) — cyclic shift offset. The second line of the description contains n space-separated integers a_i (0 ≤ a_i ≤ 1) — elements of the array.

It is guaranteed that the sum of n over all test cases does not exceed 10^6.

Output

Print t lines, each line containing the answer to the corresponding test case. The answer to a test case should be a single integer — the number of steps after which the array will contain only zeros for the first time. If there are still elements equal to 1 in the array after the end of the process, print -1.

Example

Input


5
2 1
0 1
3 2
0 1 0
5 2
1 1 0 1 0
4 2
0 1 0 1
1 1
0


Output


1
1
3
-1
0

Note

In the third sample test case the array will change as follows: 

  1. At the beginning a = [1, 1, 0, 1, 0], and a^{→ 2} = [1, 0, 1, 1, 0]. Their element-by-element "AND" is equal to $$$[1  \&  1, 1  \&  0, 0  \&  1, 1  \&  1, 0  \&  0] = [1, 0, 0, 1, 0]$$$ 
  2. Now a = [1, 0, 0, 1, 0], then a^{→ 2} = [1, 0, 1, 0, 0]. Their element-by-element "AND" equals to $$$[1  \&  1, 0  \&  0, 0  \&  1, 1  \&  0, 0  \&  0] = [1, 0, 0, 0, 0]$$$ 
  3. And finally, when a = [1, 0, 0, 0, 0] we get a^{→ 2} = [0, 0, 1, 0, 0]. Their element-by-element "AND" equals to $$$[1  \&  0, 0  \&  0, 0  \&  1, 0  \&  0, 0  \&  0] = [0, 0, 0, 0, 0]$$$ 

Thus, the answer is 3 steps.

In the fourth sample test case, the array will not change as it shifts by 2 to the right, so each element will be calculated as 0  \&  0 or 1  \&  1 thus not changing its value. So the answer is -1, the array will never contain only zeros.
							/*
							ID: abdelra29
		LANG: JAVA
		PROG: zerosum
							*/
								/*
								TO LEARN
						
								2-euler tour
							
								*/
								/*
								TO SOLVE 
								*/
								/*
								bit manipulation shit
								1-Computer Systems: A Programmer's Perspective
								2-hacker's delight
								*/
								/*
								TO WATCH
								
								*/
								            import java.util.*;
										    import java.math.*;
										    import java.io.*; 
										    import java.text.DecimalFormat;
										    import java.util.stream.Collectors;


										       public class A{
								            static FastScanner scan=new FastScanner();
											     public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
				static int dp[][];
				static char board[][];
				static int N,M;
				static int cal(int x1,int y1,int x2,int y2){
				return	dp[x2][y2]
				- dp[x1-1][y2]
				- dp[x2][y1-1]
				+ dp[x1-1][y1-1];
				}
static void pre()
{
	for (int i = 1; i <= N; i++) {
		for (int j = 1; j <= M; j++) {
			dp[i][j] = (board[i][j]-'0')
						+ dp[i - 1][j]
						+ dp[i][j - 1]
						- dp[i - 1][j - 1];
		}
	}
}
				public static void main(String[] args)  throws Exception 
								      {
								 /*
								 very important tips 
								 1-just fucking think backwards once in your shitty life
								 2-consider brute forcing and finding some patterns and observations
								 3-when you're in contest don't get out because you think there is no enough time
								 4-don't get stuck on one approach 
								 */
							   
	//			scan=new FastScanner("D:\\usaco test data\\WW.txt");
	//			out = new PrintWriter("D:\\usaco test data\\WWW.txt");

							
										 							 /*
										 READING 
								
										 3-Introduction to DP with Bit-masking codeforces
										 4-Bit Manipulation hacker-earth
										 5-read more about mobious and inclusion-exclusion 
					 				     6-read more about Fermat little theorem
										 */
										 /*
										   
										 */

					 			
								//	System.out.println((int)(2*(1e9)));      
	int tt=1;
/*	long cnt=0;
for(int i=0;i<400;i++)
{
	for(int j=0;j<400;j++)
	{
		for(int l=0;l<400;l++)
		{
			for(int k=0;k<400;k++)
			{
				cnt++;
			}
		}
	}
}
System.out.println(cnt);*/
									tt=scan.nextInt();
									int T=tt;
									 outer:while(tt-->0)
									    {
									    int n=scan.nextInt(),d=scan.nextInt();
									    ArrayDeque<Integer>deq=new ArrayDeque<Integer>();
									    int arr[]=new int[n];
									    for(int i=0;i<n;i++){
									    	arr[i]=scan.nextInt();
									    	if(arr[i]==0)
									    		deq.add(i);
									    }
									    int dist[]=new int[n];
									    Arrays.fill(dist,10000_0000);
									    for(int i:deq)
									    	dist[i]=0;
									    while(!deq.isEmpty())
									    {
									    	int p=deq.pollFirst();
									    	if(arr[(p+n-d)%n]==1)
									    	{
									    		arr[(p+n-d)%n]=0;
									    		dist[(p+n-d)%n]=dist[p]+1;
									    		deq.add((p+n-d)%n);
									    	}
									    }
									    int max=0;
									    for(int i=0;i<n;i++)
									    {
									    	if(arr[i]==1)
									    	{
									    		out.println(-1);
									    		continue outer;
									    	}
									    	max=Math.max(max,dist[i]);
									    }
									    out.println(max);





									    									    	
	  			   	
		 }							
		
	        

				out.close();
							}
							
							

							static class special implements Comparable<special>{
							int cnt,idx;
							String s;
							public special(int cnt,int idx,String s)
							{
								this.cnt=cnt;
								this.idx=idx;
								this.s=s;
							}

								 @Override
										            public int hashCode() {
										                return (int)42;
										            }
								  @Override
										            public boolean equals(Object o){
										            //	System.out.println("FUCK");
										                if (o == this) return true;
										                if (o.getClass() != getClass()) return false;
										                special t = (special)o;
										                return t.cnt == cnt && t.idx == idx;
										            }
										            public int compareTo(special o1)
										            {
										            	if(o1.cnt==cnt)
										            	{
										            		return o1.idx-idx;
										            	}
										            	return o1.cnt-cnt;
										            }
							}
				
										   
										     static long binexp(long a,long n)
										    {
										        if(n==0)
										            return 1;
										        long res=binexp(a,n/2);
										        if(n%2==1)
										            return res*res*a;
										        else 
										            return res*res;
										    }
										     
										    static long powMod(long base, long exp, long mod) {
										           if (base == 0 || base == 1) return base;
										           if (exp == 0) return 1;
										           if (exp == 1) return (base % mod+mod)%mod;
										           long R = (powMod(base, exp/2, mod) % mod+mod)%mod;
										           R *= R;
										           R %= mod;
										           if ((exp & 1) == 1) {
										               return (base * R % mod+mod)%mod;
										           }
										           else return (R %mod+mod)%mod;
										       }
										    static double dis(double x1,double y1,double x2,double y2)
										    {
										        return Math.sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
										    }
										    static long mod(long x,long y)
										        {
										            if(x<0)
										                x=x+(-x/y+1)*y;
										            return x%y;
										        }
										     public static  long pow(long b, long e) {
										                long r = 1;
										                while (e > 0) {
										                    if (e % 2 == 1) r = r * b ;
										                    b = b * b;
										                    e >>= 1;
										                }
										                return r;
										            }
										    private static void sort(int[] arr) {
										            List<Integer> list = new ArrayList<>();
										            for (int object : arr) list.add(object);
										            Collections.sort(list);
										        //Collections.reverse(list);
										            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
										        }
										    private static void sort2(long[] arr) {
										            List<Long> list = new ArrayList<>();
										            for (Long object : arr) list.add(object);
										            Collections.sort(list);
										        Collections.reverse(list);
										            for (int i = 0; i < list.size(); ++i) arr[i] = list.get(i);
										        }
										     static class FastScanner
								{
								    private int BS = 1 << 16;
								    private char NC = (char) 0;
								    private byte[] buf = new byte[BS];
								    private int bId = 0, size = 0;
								    private char c = NC;
								    private double cnt = 1;
								    private BufferedInputStream in;
								 
								    public FastScanner() {
								        in = new BufferedInputStream(System.in, BS);
								    }
								 
								    public FastScanner(String s) {
								        try {
								            in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
								        } catch (Exception e) {
								            in = new BufferedInputStream(System.in, BS);
								        }
								    }
								 
								    private char getChar() {
								        while (bId == size) {
								            try {
								                size = in.read(buf);
								            } catch (Exception e) {
								                return NC;
								            }
								            if (size == -1) return NC;
								            bId = 0;
								        }
								        return (char) buf[bId++];
								    }
								 
								    public int nextInt() {
								        return (int) nextLong();
								    }
								 
								    public int[] nextInts(int N) {
								        int[] res = new int[N];
								        for (int i = 0; i < N; i++) {
								            res[i] = (int) nextLong();
								        }
								        return res;
								    }
								 
								    public long[] nextLongs(int N) {
								        long[] res = new long[N];
								        for (int i = 0; i < N; i++) {
								            res[i] = nextLong();
								        }
								        return res;
								    }
								 
								    public long nextLong() {
								        cnt = 1;
								        boolean neg = false;
								        if (c == NC) c = getChar();
								        for (; (c < '0' || c > '9'); c = getChar()) {
								            if (c == '-') neg = true;
								        }
								        long res = 0;
								        for (; c >= '0' && c <= '9'; c = getChar()) {
								            res = (res << 3) + (res << 1) + c - '0';
								            cnt *= 10;
								        }
								        return neg ? -res : res;
								    }
								 
								    public double nextDouble() {
								        double cur = nextLong();
								        return c != '.' ? cur : cur + nextLong() / cnt;
								    }
								 
								    public double[] nextDoubles(int N) {
								        double[] res = new double[N];
								        for (int i = 0; i < N; i++) {
								            res[i] = nextDouble();
								        }
								        return res;
								    }
								 
								    public String next() {
								        StringBuilder res = new StringBuilder();
								        while (c <= 32) c = getChar();
								        while (c > 32) {
								            res.append(c);
								            c = getChar();
								        }
								        return res.toString();
								    }
								 
								    public String nextLine() {
								        StringBuilder res = new StringBuilder();
								        while (c <= 32) c = getChar();
								        while (c != '\n') {
								            res.append(c);
								            c = getChar();
								        }
								        return res.toString();
								    }
								 
								    public boolean hasNext() {
								        if (c > 32) return true;
								        while (true) {
								            c = getChar();
								            if (c == NC) return false;
								            else if (c > 32) return true;
								        }
								    }
								}

										     static class Pair implements Comparable<Pair>{
										            public long x, y,z;
										            public Pair(long x1, long y1,long z1) {
										                x=x1;
										                y=y1;
										                z=z1;
										            }
										             public Pair(long x1, long y1) {
										                x=x1;
										                y=y1;
										    
										            }
										            
										            @Override
										            public int hashCode() {
										                return (int)(x + 31 * y);
										            }
										            public String toString() {
										                return x + " " + y+" "+z;
										            }
										            @Override
										            public boolean equals(Object o){
										                if (o == this) return true;
										                if (o.getClass() != getClass()) return false;
										                Pair t = (Pair)o;
										                return t.x == x && t.y == y&&t.z==z;
										            }
										    public int compareTo(Pair o)
										    {
										    								  	
										  if(x==o.x)
										  	return (int)(y-o.y);
										    	return (int)(x-o.x);
										     
										        }
										     
										    }
										}
										
										    
										   

										     
