Problem: Phoenix has n blocks of height h_1, h_2, ..., h_n, and all h_i don't exceed some value x. He plans to stack all n blocks into m separate towers. The height of a tower is simply the sum of the heights of its blocks. For the towers to look beautiful, no two towers may have a height difference of strictly more than x. 

Please help Phoenix build m towers that look beautiful. Each tower must have at least one block and all blocks must be used.

Input

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

The first line of each test case contains three integers n, m, and x (1 ≤ m ≤ n ≤ 10^5; 1 ≤ x ≤ 10^4) — the number of blocks, the number of towers to build, and the maximum acceptable height difference of any two towers, respectively. 

The second line of each test case contains n space-separated integers (1 ≤ h_i ≤ x) — the heights of the blocks. 

It is guaranteed that the sum of n over all the test cases will not exceed 10^5.

Output

For each test case, if Phoenix cannot build m towers that look beautiful, print NO. Otherwise, print YES, followed by n integers y_1, y_2, ..., y_n, where y_i (1 ≤ y_i ≤ m) is the index of the tower that the i-th block is placed in.

If there are multiple solutions, print any of them.

Example

Input


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


Output


YES
1 1 1 2 2
YES
1 2 2 3

Note

In the first test case, the first tower has height 1+2+3=6 and the second tower has height 1+2=3. Their difference is 6-3=3 which doesn't exceed x=3, so the towers are beautiful.

In the second test case, the first tower has height 1, the second tower has height 1+2=3, and the third tower has height 3. The maximum height difference of any two towers is 3-1=2 which doesn't exceed x=3, so the towers are beautiful.

Solution (in JAVA):

Solution:
import java.util.*;
import java.util.Map.Entry;


import java.io.*;
import java.math.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
	
	public static void main (String[] args) throws IOException
	{
		final long mod=(long) (1e9+7);  
		Reader s=new Reader();
		  PrintWriter pt=new PrintWriter(System.out);
		  
//		  BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		  int T=s.nextInt();
//		  int T=Integer.parseInt(br.readLine());
//		  int T=1;
		  while(T-->0)
		  {
//		        int n=s.nextInt();
//		        int m=s.nextInt();
//		        long x=s.nextLong();
//		        ArrayList<Pair> h=new ArrayList<Pair>();
//		        for(int i=0;i<n;i++) {
//		        	h.add(new Pair(s.nextInt(), i+1));
//		        }
//		        Collections.sort(h, Collections.reverseOrder());
//		        PriorityQueue<Pair> pq = new PriorityQueue<Pair>();
//		        int ans[]=new int[n];
//		        for(int i=0;i<m;i++) {
//		        	pq.add(new Pair(h.get(i).a, i));
//		        	ans[i]=i+1;
//		        }
//		        
//		        
//		        for(int i=m;i<n;i++) {
//		        	Pair p = pq.poll();
////		        	p.a+=h.get(i).a;
//		        	ans[h.get(i).b-1]=p.b+1;
//		        	pq.add(new Pair(p.a+h.get(i).a, p.b));
//		        }
//		        
//		        	pt.println("YES");
//		        	for(int i=0;i<n;i++) {
//		        		pt.print(ans[i]+" ");
//		        	}
//		        	pt.println();
			  
			  
			  int n = s.nextInt();
	            int m = s.nextInt();
	            int x = s.nextInt();
	            int a[] = new int[n];
	            ArrayList<Pair> pp = new ArrayList<Pair>();
	            for(int i=0;i<n;i++){
	                a[i] = s.nextInt();
	                pp.add(new Pair(a[i], i));
	            }
	            PriorityQueue<Pair> p = new PriorityQueue<>((x1,y1)->x1.a-y1.a);
	            for(int i=0;i<m;i++){
	                p.add(new Pair(0,i));
	            }
	            Collections.sort(pp);
	            int b[] = new int[n];
	            for(int i=n-1;i>=0;i--){
	                Pair val = p.poll();
	                b[pp.get(i).b] = val.b;
	                p.add(new Pair(val.a+pp.get(i).a,val.b));
	            }
	            pt.println("YES");
	            for(int i=0;i<n;i++){
	                pt.print((b[i]+1)+" ");
	            }
	            pt.println();

		        
		        
		        
		  }
		  pt.close();
	}
	
	static void divideBy2(int arr[], int n) {
		for(int i=0;i<n;i++) {
			arr[i]=arr[i]>>1;
		}
	}
	
	static boolean isEven(int arr[], int n) {
		for(int i=0;i<n;i++) {
			if(arr[i]%2==1)
				return false;
		}
		return true;
	}
	
	static boolean isPartition(int arr[], int n) {
		int sum = 0;
	    int i, j;
	 
	    // Calculate sum of all elements
	    for (i = 0; i < n; i++)
	        sum += arr[i];
	 
	    if (sum % 2 != 0)
	        return false;
	 
	    boolean part[][]=new boolean[sum/2+1][n+1];
	 
	    // initialize top row as true
	    for (i = 0; i <= n; i++)
	        part[0][i] = true;
	 
	    // initialize leftmost column, except part[0][0], as false
	    for (i = 1; i <= sum / 2; i++)
	        part[i][0] = false;
	 
	    // Fill the partition table in bottom up manner
	    for (i = 1; i <= sum / 2; i++) {
	        for (j = 1; j <= n; j++) {
	            part[i][j] = part[i][j - 1];
	            if (i >= arr[j - 1])
	                part[i][j] = part[i][j]
	                             || part[i - arr[j - 1]][j - 1];
	        }
	    }
	    return part[sum / 2][n];
	}
	
	static int setBit(int S, int j) { return S | 1 << j; }

	static int clearBit(int S, int j) { return S & ~(1 << j); }

	static int toggleBit(int S, int j) { return S ^ 1 << j; }

	static boolean isOn(int S, int j) { return (S & 1 << j) != 0; }

	static int turnOnLastZero(int S) { return S | S + 1; }
	
	static int turnOnLastConsecutiveZeroes(int S) { return S | S - 1; }
	
	static int turnOffLastBit(int S) { return S & S - 1; }
	
	static int turnOffLastConsecutiveBits(int S) { return S & S + 1; }

	static int lowBit(int S) { return S & -S; }

	static int setAll(int N) { return (1 << N) - 1; }

	static int modulo(int S, int N) { return (S & N - 1); }		 //S%N, N is a power of 2

	static boolean isPowerOfTwo(int S) { return (S & S - 1) == 0; }
	
	static boolean isWithin(long x, long y, long d, long k) {
		return x*k*x*k + y*k*y*k <= d*d;
	}
	
	static long modFact(long n, 
            long p) 
	{ 
		if (n >= p) 
		 return 0; 
		
		long result = 1; 
		for (int i = 1; i <= n; i++) 
		 result = (result * i) % p; 
		
		return result; 
	} 
	static int sum(int[] arr, int n)
	{
	    int inc[]=new int[n+1];
	    int dec[]=new int[n+1];
	    inc[0] = arr[0];
	    dec[0] = arr[0];

	    for (int i = 1; i < n; i++) {
	        for (int j = 0; j < i; j++) {
	            if (arr[j] > arr[i]) {
	                dec[i] = max(dec[i], inc[j] + arr[i]);
	            }
	            else if (arr[i] > arr[j]) {
	                inc[i] = max(inc[i], dec[j] + arr[i]);
	            }
	        }
	    }
	    return max(inc[n - 1], dec[n - 1]);
	}
	static long nc2(long a) {
		return a*(a-1)/2;
	}
	public static int numberOfprimeFactors(int n) 
    { 
        // Print the number of 2s that divide n 
		HashSet<Integer> hs = new HashSet<Integer>();
        while (n%2==0) 
        { 
            hs.add(2);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (int i = 3; i <= Math.sqrt(n); i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                hs.add(i);
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            hs.add(n);
        return hs.size();
    } 
	static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 




	

	static void reverse(int arr[],int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static void reverse(long arr[],int start, int end) 
	{ 
		long temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}  
	static boolean isPrime(int n) 
    { 
        // Corner cases 
        if (n <= 1) return false; 
        if (n <= 3) return true; 
      
        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n % 2 == 0 || n % 3 == 0) return false; 
      
        for (int i = 5; i * i <= n; i = i + 6) 
            if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
      
        return true; 
    } 
	static int p2(int n) {
		int k=0;
		while(n>1) {
			if(n%2!=0)
				return k;
			n/=2;
			k++;
		}
		return k;
	}
	static boolean isp2(int n) {
		while(n>1) {
			if(n%2==1)
				return false;
			n/=2;
		}
		return true;
	}
	static int binarySearch(int arr[], int first, int last, int key){  
		   int mid = (first + last)/2;  
		   while( first <= last ){  
		      if ( arr[mid] < key ){  
		        first = mid + 1;     
		      }else if ( arr[mid] == key ){  
		        return mid;  
		      }else{  
		         last = mid - 1;  
		      }  
		      mid = (first + last)/2;  
		   }  
		   return -1;
		 }  

	static void print(int a[][]) {
		for(int i=0;i<a.length;i++)
		{
			for(int j=0;j<a[0].length;j++)
				System.out.print(a[i][j]+" ");
			System.out.println();
		}
	}
	static int max (int x, int y) {
		return (x > y)? x : y;
	} 
	static int search(Pair[] p, Pair pair) {
		int l=0, r=p.length;
		while (l <= r) { 
	        int m = l + (r - l) / 2;
	        if (p[m].compareTo(pair)==0) 
	            return m; 
	        if (p[m].compareTo(pair)<0) 
	            l = m + 1; 
	        else
	            r = m - 1;
	    }
	    return -1;
	}
	static void pa(int a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void pa(long a[])
	{
		for(int i=0;i<a.length;i++)
			System.out.print(a[i]+" ");
		System.out.println();
		
	}
	static void reverseArray(int arr[], 
            int start, int end) 
	{ 
		int temp; 
		   
		while (start < end) 
		{ 
		    temp = arr[start];  
		    arr[start] = arr[end]; 
		    arr[end] = temp; 
		    start++; 
		    end--; 
		}  
	}     
	static boolean isPalindrome(String s) {
		int l=s.length();
		for(int i=0;i<l/2;i++)
		{
			if(s.charAt(i)!=s.charAt(l-i-1))
				return false;
		}
		return true;
	}
	static long nc2(long n, long m) {
		return (n*(n-1)/2)%m;
	}
	static long c(long a) {
		return a*(a+1)/2;
	}
	static int next(long[] arr, long target)  
    {  
        int start = 0, end = arr.length - 1;  
    
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;  
    
            // Move to right side if target is  
            // greater.  
            if (arr[mid] < target) {
                start = mid + 1;  
            }  
    
            // Move left side.  
            else {  
                ans = mid;  
                end = mid - 1;  
            }  
        }  
        return ans;  
    } 
	
	static int prev(long[] arr, long target)  
    {  
        int start = 0, end = arr.length - 1;  
    
        int ans = -1;  
        while (start <= end) {  
            int mid = (start + end) / 2;  
    
            // Move to left side if target is  
            // lesser.  
            if (arr[mid] > target) {
                end = mid - 1;  
            }  
    
            // Move right side.  
            else {  
                ans = mid;  
                start = mid + 1;  
            }  
        }  
        return ans;  
    } 

	static long power(long x, long y, long p) 
    { 
        long res = 1; 
        x = x % p; 
                      
        while (y > 0) 
        { 
            if (y % 2 == 1) 
                res = (res * x) % p; 
            y = y >> 1;
            x = (x * x) % p; 
        } 
        return  res; 
    } 
    static long modInverse(long n, long p) 
    { 
        return power(n, p-2, p); 
    } 
    static long nCrModP(long n, long r, 
                                    long p) 
    { 
        if(r>n)
        	return 0;
    	if (r == 0) 
            return 1; 
        long[] fac = new long[(int) (n+1)]; 
        fac[0] = 1; 
        for (int i = 1 ;i <= n; i++) 
            fac[i] = fac[i-1] * i % p;
        return (fac[(int) n]* modInverse(fac[(int) r], p) 
                % p * modInverse(fac[(int) (n-r)], p) 
                                    % p) % p; 
    } 
	static String reverse(String str)
	{
		return new StringBuffer(str).reverse().toString();
	}



	static long fastpow(long x, long y, long m)  
    { 
        if (y == 0) 
            return 1; 
          
        long p = fastpow(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
	
	static boolean isPerfectSquare(long l)
	{
		return Math.pow((long)Math.sqrt(l),2)==l;
	}
	
	
	static void merge(long[] arr, int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        long L[] = new long [n1]; 
        long R[] = new long [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
	static void merge(int arr[], int l, int m, int r) 
    { 
        // Find sizes of two subarrays to be merged 
        int n1 = m - l + 1; 
        int n2 = r - m; 
  
        /* Create temp arrays */
        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
  
        /*Copy data to temp arrays*/
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
  
  
        /* Merge the temp arrays */
  
        // Initial indexes of first and second subarrays 
        int i = 0, j = 0; 
  
        // Initial index of merged subarry array 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
  
        /* Copy remaining elements of L[] if any */
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
  
        /* Copy remaining elements of R[] if any */
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
  
    // Main function that sorts arr[l..r] using 
    // merge() 
    static void sort(long arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            // Find the middle point 
            int m = (l+r)/2; 
  
            // Sort first and second halves 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
  
            // Merge the sorted halves 
            merge(arr, l, m, r); 
        } 
    } 
    static class Pair implements Comparable<Pair>{
        int a;
        int b;
        Pair(int a,int b){
            this.a=a;
 
            this.b=b;
        }   
        public int compareTo(Pair p){
            if(a>p.a)
                return 1;
            if(a==p.a)
                return (b-p.b);
            return -1;
        }
    }
	static class Reader 
    { 
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[128]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
}