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.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;


public class Main{

    static long MOD = 1_000_000_007L;
    //static long MOD = 998_244_353L;
    //static long MOD = 1_000_000_033L;
    static long inv2 = (MOD + 1) / 2;

    static int[][] dir = new int[][]{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
    static long lMax = 0x3f3f3f3f3f3f3f3fL;
    static int iMax = 0x3f3f3f3f;
    static HashMap <Long, Long> memo = new HashMap();
    static MyScanner sc = new MyScanner();
    //static ArrayList <Integer> primes;

    static int nn = 300000;
    static long[] pow2;
    static long [] fac;
    static long [] pow;
    static long [] inv;
    static long [] facInv;
    static int[] base;
    static int[] numOfDiffDiv;
    static int[] numOfDiv;
    static ArrayList <Integer> primes;
    //static int[] primes;
    static int ptr = 0;
    static boolean[] isPrime;

    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
    public static void main(String[] args) {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        // Start writing your solution here. -------------------------------------



        /*fac = new long[nn + 1];
        fac[1] = 1;
        for(int i = 2; i <= nn; i++)
            fac[i] = fac[i - 1] * i % MOD;*/


        /*pow2 = new long[nn + 1];
        pow2[0] = 1L;
        for(int i = 1; i <= nn; i++)
            pow2[i] = pow2[i - 1] * 2L;*/


        /*inv = new long[nn + 1];
        inv[1] = 1;
        for (int i = 2; i <= nn; ++i)
            inv[i] = (MOD - MOD / i) * inv[(int)(MOD % i)] % MOD;*/

        /*facInv = new long[nn + 1];
        facInv[0] = facInv[1] = 1;
        for (int i = 2; i <= nn; ++i)
            facInv[i] = facInv[i - 1] * inv[i] % MOD;*/


        /*numOfDiffDiv = new int[nn + 1];
        for(int i = 2; i <= nn; i++)
            if(numOfDiffDiv[i] == 0)
                for(int j = i; j <= nn; j += i)
                    numOfDiv[j] ++;*/

        /*numOfDiv = new int[nn + 1];
        numOfDiv[1] = 1;
        for(int i = 2; i <= nn; i++) {
            for(int j = 2; j * j <= i; j++) {
                if(i % j == 0) {
                    numOfDiv[i] = numOfDiv[i / j] + 1;
                    break;
                }
            }
        }*/

        //primes = sieveOfEratosthenes(100001);

        /*
        int t = 1;
        //t = sc.ni();
        while(t-- > 0) {
            //boolean res = solve();
            //out.println(res ? "YES" : "NO");
            long res = solve();
            out.println(res);
        }*/


        int t = 1, tt = 0;
        t = sc.ni();
        for(int i = 1; i <40000; i++) squares.add(i * i);
        while(tt++ < t) {
            boolean res = solve();
            //out.println("Case #" + tt + ": " + res);
            //out.println(res ? "YES" : "NO");
        }
        out.close();
    }
    static HashSet <Integer> squares = new HashSet();

    static boolean solve() {
        /*String s = sc.nextLine();
        char[] c = s.toCharArray();
        int n = c.length;*/
        //int n = sc.ni();
        //long[] a =  new long[n];
        //for(int i = 0; i < n; i++) a[i] = sc.nl();
        long res = 0;
        int n = sc.ni(), m = sc.ni(), x = sc.ni();
        int[] a = new int[n];
        for(int i = 0; i < n; i++) a[i] = sc.ni();
        PriorityQueue <int[]> pq = new PriorityQueue<>((p1, p2) -> p1[1] - p2[1]);
        out.println("YES");
        for(int i = 0; i < m; i++) {
            pq.add(new int[]{i, a[i]});
            out.print((i + 1) + " ");
        }
        for(int i = m; i < n; i++) {
            int[] tmp = pq.poll();
            out.print((tmp[0] + 1) + " ");
            tmp[1] += a[i];
            pq.add(tmp);
        }
        out.println();
        return false;
    }

    // edges to adjacency list by uwi
    public static int[][] packU(int n, int[] from, int[] to) {
        return packU(n, from, to, from.length);
    }

    public static int[][] packU(int n, int[] from, int[] to, int sup) {
        int[][] g = new int[n][];
        int[] p = new int[n];
        for (int i = 0; i < sup; i++) p[from[i]]++;
        for (int i = 0; i < sup; i++) p[to[i]]++;
        for (int i = 0; i < n; i++) g[i] = new int[p[i]];
        for (int i = 0; i < sup; i++) {
            g[from[i]][--p[from[i]]] = to[i];
            g[to[i]][--p[to[i]]] = from[i];
        }
        return g;
    }

    // tree diameter by uwi
    public static int[] diameter(int[][] g) {
        int n = g.length;
        int f0 = -1, f1 = -1, d01 = -1;
        int[] q = new int[n];
        boolean[] ved = new boolean[n];
        {
            int qp = 0;
            q[qp++] = 0; ved[0] = true;
            for(int i = 0;i < qp;i++){
                int cur = q[i];
                for(int e : g[cur]){
                    if(!ved[e]){
                        ved[e] = true;
                        q[qp++] = e;
                        continue;
                    }
                }
            }
            f0 = q[n-1];
        }
        {
            int[] d = new int[n];
            int qp = 0;
            Arrays.fill(ved, false);
            q[qp++] = f0; ved[f0] = true;
            for(int i = 0;i < qp;i++){
                int cur = q[i];
                for(int e : g[cur]){
                    if(!ved[e]){
                        ved[e] = true;
                        q[qp++] = e;
                        d[e] = d[cur] + 1;
                        continue;
                    }
                }
            }
            f1 = q[n-1];
            d01 = d[f1];
        }
        return new int[]{d01, f0, f1};
    }

    public static long c(int n, int k) {
        return (fac[n] * facInv[k] % MOD) * facInv[n - k] % MOD;
    }


    // SegmentTree range min/max query by uwi
    public static class SegmentTreeRMQ {
        public int M, H, N;
        public int[] st;

        public SegmentTreeRMQ(int n)
        {
            N = n;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            Arrays.fill(st, 0, M, Integer.MAX_VALUE);
        }

        public SegmentTreeRMQ(int[] a)
        {
            N = a.length;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            for(int i = 0;i < N;i++){
                st[H+i] = a[i];
            }
            Arrays.fill(st, H+N, M, Integer.MAX_VALUE);
            for(int i = H-1;i >= 1;i--)propagate(i);
        }

        public void update(int pos, int x)
        {
            st[H+pos] = x;
            for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
        }

        private void propagate(int i)
        {
            st[i] = Math.min(st[2*i], st[2*i+1]);
        }

        public int minx(int l, int r){
            int min = Integer.MAX_VALUE;
            if(l >= r)return min;
            while(l != 0){
                int f = l&-l;
                if(l+f > r)break;
                int v = st[(H+l)/f];
                if(v < min)min = v;
                l += f;
            }

            while(l < r){
                int f = r&-r;
                int v = st[(H+r)/f-1];
                if(v < min)min = v;
                r -= f;
            }
            return min;
        }

        public int min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);}

        private int min(int l, int r, int cl, int cr, int cur)
        {
            if(l <= cl && cr <= r){
                return st[cur];
            }else{
                int mid = cl+cr>>>1;
                int ret = Integer.MAX_VALUE;
                if(cl < r && l < mid){
                    ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
                }
                if(mid < r && l < cr){
                    ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
                }
                return ret;
            }
        }
    }

    public static char[] rev(char[] a){char[] b = new char[a.length];for(int i = 0;i < a.length;i++)b[a.length-1-i] = a[i];return b;}

    public static double dist(double a, double b){
        return Math.sqrt(a * a + b * b);
    }

    public static long inv(long a){
        return quickPOW(a, MOD - 2);
    }

    public class Interval {
        int start;
        int end;
        public Interval(int start, int end) {
            this.start = start;
            this.end = end;
        }
    }

    public static ArrayList<Integer> sieveOfEratosthenes(int n) {
        boolean prime[] = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p]) {
                for (int i = p * 2; i <= n; i += p) {
                    prime[i] = false;
                }
            }
        }
        ArrayList<Integer> primeNumbers = new ArrayList<>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                primeNumbers.add(i);
            }
        }
        return primeNumbers;
    }


    public static int lowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
    public static int lowerBound(int[] a, int l, int r, int v)
    {
        if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
        int low = l-1, high = r;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] >= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }
    public static int rlowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
    public static int rlowerBound(int[] a, int l, int r, int v)
    {
        if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
        int low = l-1, high = r;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] <= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }
    public static long C(int n, int m)
    {
        if(m == 0 || m == n) return 1l;
        if(m > n || m < 0) return 0l;
        long res = fac[n] * quickPOW((fac[m] * fac[n - m]) % MOD, MOD - 2) % MOD;

        return res;
    }
    public static long quickPOW(long n, long m)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % MOD;
            n = (n * n) % MOD;
            m >>= 1;
        }
        return ans;
    }
    public static long quickPOW(long n, long m, long mod)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % mod;
            n = (n * n) % mod;
            m >>= 1;
        }
        return ans;
    }

    public static int gcd(int a, int b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }
    public static long gcd(long a, long b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }

    static class Randomized {
        public static void shuffle(int[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static void shuffle(long[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return RandomWrapper.INSTANCE.nextInt(l, r);
        }
    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper(new Random());

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int ni() {
            return Integer.parseInt(next());
        }
        long nl() {
            return Long.parseLong(next());
        }
        double nd() {
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}