Problem: Phoenix has collected n pieces of gold, and he wants to weigh them together so he can feel rich. The i-th piece of gold has weight w_i. All weights are distinct. He will put his n pieces of gold on a weight scale, one piece at a time. 

The scale has an unusual defect: if the total weight on it is exactly x, it will explode. Can he put all n gold pieces onto the scale in some order, without the scale exploding during the process? If so, help him find some possible order. 

Formally, rearrange the array w so that for each i (1 ≤ i ≤ n), ∑_{j = 1}^{i}w_j ≠ x.

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 two integers n and x (1 ≤ n ≤ 100; 1 ≤ x ≤ 10^4) — the number of gold pieces that Phoenix has and the weight to avoid, respectively. 

The second line of each test case contains n space-separated integers (1 ≤ w_i ≤ 100) — the weights of the gold pieces. It is guaranteed that the weights are pairwise distinct.

Output

For each test case, if Phoenix cannot place all n pieces without the scale exploding, print NO. Otherwise, print YES followed by the rearranged array w. If there are multiple solutions, print any.

Example

Input


3
3 2
3 2 1
5 3
1 2 3 4 8
1 5
5


Output


YES
3 2 1
YES
8 1 2 3 4
NO

Note

In the first test case, Phoenix puts the gold piece with weight 3 on the scale first, then the piece with weight 2, and finally the piece with weight 1. The total weight on the scale is 3, then 5, then 6. The scale does not explode because the total weight on the scale is never 2.

In the second test case, the total weight on the scale is 8, 9, 11, 14, then 18. It is never 3.

In the third test case, Phoenix must put the gold piece with weight 5 on the scale, and the scale will always explode.

Solution (in JAVA):

Solution:
import javafx.scene.layout.Priority;
import sun.reflect.generics.tree.Tree;

import java.sql.Array;
import java.util.*;
import java.io.*;
import java.util.stream.Stream;

import static java.lang.Math.*;
public class A
{
    static InputReader in=new InputReader(System.in);
    static OutputWriter out=new OutputWriter(System.out);
    static StringBuilder sb=new StringBuilder();
    static long MOD = (long)(998244353);

    static int n;
    static int a[];

    // Main Class Starts Here
    public static void main(String args[])throws IOException
    {
        // Write your code.
        int t = in();
        while(t-->0) {
            int n = in();
            int x = in();
            int a[] = an(n);
            Arrays.sort(a);
            int sum = 0;
            boolean canDone = true;
            for(int i = 0; i < n ;i++){
                sum += a[i];
                if(sum == x){
                    if(i == n-1){
                        canDone = false;
                        break;
                    }
                    int temp = a[i];
                    a[i] = a[i+1];
                    a[i+1] = temp;
                }
            }
            if(!canDone){
                app("NO\n");
            }
            else{
                app("YES\n");
                for(int val:a){
                    app(val+" ");
                }
                app("\n");
            }
        }
        out.printLine(sb);
        out.close();
    }

    static class DisjointSet{
        int par[];
        int rank[];
        int n;
        public DisjointSet(int n){
            this.n = n;
            par = new int[n];
            rank = new int[n];
            for(int i = 0; i < n; i++){
                par[i] = i;
            }
        }

        public int findPar(int i){
            // path compression.
            if(par[i] != i){
                par[i] = findPar(par[i]);
            }
            return par[i];
        }

        public int merge(int x, int y){
            int parX = findPar(x);
            int parY = findPar(y);
            if(parX == parY) return 0; // no decrease in connected components
            if(rank[parX] > rank[parY]){
                // merge y to x.
                par[parY] = parX;
            }
            else if(rank[parY] > rank[parX]){
                par[parX] = parY;
            }
            else{
                par[parY] = parX;
                rank[parX]++;
            }
            return 1; // after merging the decrease in connected components is 1.
        }
    }

    public static class Edge{
        int from;
        int to;
        int id;
        boolean visited;
        public Edge(int from, int to, int id){
            this.from = from;
            this.to = to;
            this.id =id;
            this.visited = false;
        }
    }

    public static int[] an(int n) {
        int ar[]=new int[n];
        for(int i=0;i<n;i++)
            ar[i]=in();
        return ar;
    }

    public static long[] lan(int n) {
        long ar[]=new long[n];
        for(int i=0;i<n;i++)
            ar[i]=lin();
        return ar;
    }

    public static String atos(Object ar[]) {
        return Arrays.toString(ar);
    }

    public static int in() {
        return in.readInt();
    }

    public static long lin() {
        return in.readLong();
    }

    public static String sn() {
        return in.readString();
    }

    public static void prln(Object o) {
        out.printLine(o);
    }

    public static void prn(Object o) {
        out.print(o);
    }

    public static void display(int a[]) {
        out.printLine(Arrays.toString(a));
    }

    public static HashMap<Integer,Integer> hm(int a[]){
        HashMap<Integer,Integer> map=new HashMap<>();
        for(int i=0; i < a.length;i++) {
            int keep = (int)map.getOrDefault(a[i],0);
            map.put(a[i],++keep);
        }
        return map;
    }

    public static void app(Object o) {
        sb.append(o);
    }

    public static long calcManhattanDist(int x1,int y1,int x2,int y2) {
        long xa = Math.abs(x1-x2);
        long ya = Math.abs(y1-y2);
        return (xa+ya);
    }


    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object...objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }

        public void printLine(Object...objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }
    }
}