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.io.*;
import java.util.*;
import java.lang.*;
public class Main9{
    static InputReader sc;
    static PrintWriter pw;
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        sc = new InputReader(inputStream);
        pw = new PrintWriter(outputStream);
        solve();
        pw.close();
    }
    // static int L,R,top,bottom;
    // static int cnt,edge;
    // static long ans;
    static boolean isIsland;
    public static void solve() {
		int t=sc.nextInt();
        // int t=1;
        u:while(t-->0){ 
            int n=s(0);
            int m=s(0);
            int x=s(0);
            long []arr=new long [n];
            feedArr(arr);
            List<long[]>list=new ArrayList<>();
            for(int i=0;i<n;i++)
                list.add(new long[]{i,arr[i]});
            Collections.sort(list,(a,b)->a[1]==b[1]?0:((a[1]-b[1])<0?-1:1));
            PriorityQueue<long[]> pq=new PriorityQueue<>((a,b)->a[1]==b[1]?0:(a[1]-b[1]<0?-1:1));
            int []ans=new int [n];
            for(int i=1;i<=m;i++){
                pq.offer(new long []{i,list.get(n-i)[1]});
                ans[(int)list.get(n-i)[0]]=i;
            }
            // long max=arr[n-1];
            long []pr;
            for(int i=n-m-1;i>=0;i--){
                pr=pq.poll();
                pr[1]+=list.get(i)[1];
                ans[(int)list.get(i)[0]]=(int)pr[0];
                // max=Math.max(max,pr[1]);
                pq.offer(pr);
            }
            // if(max-pq.peek()[1]>x){
            //     pln("NO");
            //     continue u;
            // }
            pln("YES");
            for(int i:ans)
                p(i+" ");
            pln("");
        }
    }
    static void update_DAG(int cur,int val, int []graph, int n)
    {
        if(val>maxx[cur])
        {
            int x=graph[cur];
            if(x!=-1)
                update_DAG(x,val+1,graph,n);
            maxx[cur]=val;
            update(cur,val,n);
        }
    }
    static int []bit, maxx;
    static void update(int i,int val, int n)
    {
        while(i<=n)
        {
            bit[i]=Math.max(bit[i],val);
            i=i+(i&(-i));
        }
    }
    static int query(int i)
    {
        int ret=0;
        while(i>0)
        {
            ret=Math.max(ret,bit[i]);
            i=i-(i&(-i));
        }
        return ret;
    }    
    public static int [][]dir=new int [][]{{1,0},{0,1},{-1,0},{0,-1}};        
    public static int find(List<Integer> list, int x){
        int l=0,r=list.size()-1,m;
        while(l<=r){
            m=(r-l)/2+l;
            if(list.get(m)<=x)
                l=m+1;
            else
                r=m-1;
        }
        return r;
    } 
    static class Node{
        int val;
        long cost;
        Node next;
        Node(int v,long c){
            val=v;
            next=null;
            cost=c;
        }
    }    
    public static long sum(long n){
        long val=0l;
        while(n>0){
            val+=n%10;
            n/=10;
        }
        return val;
    }
    // static class Node{
    //     int left,right;
    //     Node prev,next;
    //     Node(int i, int v){
    //         left=i;
    //         right=v;
    //         prev=next=null;
    //     }
    //     void remove(){
    //         this.prev.next=this.next;
    //         this.next.prev=this.prev;
    //     }
    //     void insert(Node node){
    //         node.next=this;
    //         node.prev=this.prev;
    //         node.prev.next=node;
    //         this.prev=node;
    //     }
    // } 
    public static int  findDiameter(int r, List<List<Integer>>list){
        return findFarthest(findFarthest(r,list)[0],list)[1];
    }
    public static int[] findFarthest(int u, List<List<Integer>>list){
        int n=list.size();
        boolean []vis=new boolean[n+1];
        Queue<Integer>q=new LinkedList<>();
        q.offer(u);
        vis[u]=true;
        int s,pr,cnt=0;
        int []ar=new int[]{u,0};
        while(q.size()>0){
            s=q.size();
            while(s-->0){
                pr=q.poll();
                if(ar[1]<cnt){
                    ar[1]=cnt;
                    ar[0]=pr;
                }
                for(int i:list.get(pr)){
                    if(!vis[i]){
                        vis[i]=true;
                        q.offer(i);
                    }
                }
            }
            cnt++;
        }
        return ar;
    }
    public static long atMostK(char []chrr, int k){
        if(k<0)
            return 0;
        int l=0,cnt=0;
        long ans=0l;
        for(int i=0;i<chrr.length;i++){
            if(chrr[i]=='1')
                cnt++;
            while(cnt>k){
                if(chrr[l++]=='1')
                    cnt--;
            }
            ans+=(long)(i-l)+1l;
        }
        return ans;
    }
    public static int ask(int l){
        System.out.println(l);
        System.out.flush();
        return sc.nextInt();
    }
    public static void sort(int []arr){
        ArrayList<Integer> list=new ArrayList<>();
        for(int i=0;i<arr.length;i++)
            list.add(arr[i]);
        Collections.sort(list);
        for(int i=0;i<arr.length;i++)
            arr[i]=list.get(i);
    }
    public static void sort(long []arr){
        ArrayList<Long> list=new ArrayList<>();
        for(int i=0;i<arr.length;i++)
            list.add(arr[i]);
        Collections.sort(list);
        for(int i=0;i<arr.length;i++)
            arr[i]=list.get(i);
    }
    public static void swap(char []chrr, int i, int j){
        char temp=chrr[i];
        chrr[i]=chrr[j];
        chrr[j]=temp;
    }
    public static int countSetBits(long n){
        int a=0;
        while(n>0){
            a+=(n&1);
            n>>=1;
        }
        return a;
    }
    static class Pair{
        int v,w;
        Pair(int W, int V){
            v=V;
            w=W;
        }
     //*
    }
    /*/
        public int compareTo(Pair p){
            return (b-p.b);
        }
        public int hashCode(){
            int hashcode = (a+" "+b).hashCode();
            return hashcode;
        }
        public boolean equals(Object obj){
            if (obj instanceof Pair) {
                Pair p = (Pair) obj;
                return (p.a==this.a && p.b == this.b);
            }
            return false;
        }
    }
    //*/
    static boolean isPrime(long n) { 
        if (n <= 1) 
            return false; 
        if (n <= 3) 
            return true; 
        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 long gcd(long a, long b) { 
        if (b == 0) 
            return a; 
        return a>b?gcd(b, a % b):gcd(a, b % a);  
    } 
    static long fast_pow(long base,long n,long M){
        if(n==0)
           return 1;
        if(n==1)
        return base;
        long halfn=fast_pow(base,n/2,M);
        if(n%2==0)
            return ( halfn * halfn ) % M;
        else
            return ( ( ( halfn * halfn ) % M ) * base ) % M;
    }
    static long modInverse(long n,long M){
        return fast_pow(n,M-2,M);
    }
    public static int s(int n){
        return sc.nextInt();
    }
    public static long s(long n){
        return sc.nextLong();
    }
    public static String s(String n){
        return sc.next();
    }
    public static double s(double n){
        return sc.nextDouble();
    }
    public static void p(int n){
        pw.print(n);
    }
    public static void p(long n){
        pw.print(n);
    }
    public static void p(String n){
        pw.print(n);
    }
    public static void p(double n){
        pw.print(n);
    }
    public static void pln(int n){
        pw.println(n);
    }
    public static void pln(long n){
        pw.println(n);
    }
    public static void pln(String n){
        pw.println(n);
    }
    public static void pln(double n){
        pw.println(n);
    }
    public static void feedArr(long []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextLong();
    }
    public static void feedArr(double []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextDouble();
    }
    public static void feedArr(int []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.nextInt();
    }
    public static void feedArr(String []arr){
        for(int i=0;i<arr.length;i++)
            arr[i]=sc.next();
    }
    public static String printArr(int []arr){
        StringBuilder sbr=new StringBuilder();
        for(int i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public  static String printArr(long []arr){
        StringBuilder sbr=new StringBuilder();
        for(long i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(String []arr){
        StringBuilder sbr=new StringBuilder();
        for(String i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    public static String printArr(double []arr){
        StringBuilder sbr=new StringBuilder();
        for(double i:arr)
            sbr.append(i+" ");
        return sbr.toString();
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
 
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}