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 java.io.*;
import java.util.*;
import java.util.concurrent.ConcurrentHashMap;

public class Main {
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int t=sc.nextInt();
        while (t-->=1){
            int n=sc.nextInt(),x=sc.nextInt();
            int a[]=sc.readArray(n);
            long sum=0;
            for (int i=0;i<n;i++)sum+=a[i];
            if (sum==x){
                System.out.println("NO");
            }
            else{
                int ans[]=new int[n];
                sum=0;
                int ind=-1;
                sort(a);
                boolean f=true;
                for (int i=0;i<n-1;i++){
                    if (sum+a[i]==x){
                        ans[i]=a[n-1];
                        ans[n-1]=a[i];
                        f=false;
                    }
                    else{
                        sum+=a[i];
                        ans[i]=a[i];
                    }
                }
                if (f)ans[n-1]=a[n-1];
                System.out.println("YES");
                printArray(ans);
                System.out.println();
            }
        }
    }



//        out.flush();



    //------------------------------------if-------------------------------------------------------------------------------------------------------------------------------------------------
    //sieve
    static void primeSieve(int a[]){
        //mark all odd number as prime
        for (int i=3;i<a.length;i+=2){
            a[i]=1;
        }
        for (long i=3;i<a.length;i+=2){
            //if the number is marked then it is prime
            if (a[(int) i]==1){
                //mark all muliple of the number as not prime
                for (long j=i*i;j<a.length;j+=i){
                    a[(int)j]=0;
                }
            }
        }
        a[2]=1;
        a[1]=a[0]=0;
    }
    static void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    static String sortString(String s) {
        char temp[] = s.toCharArray();
        Arrays.sort(temp);
        return new String(temp);
    }
    static class Pair implements Comparable<Pair> {
        int a;
        int b;

        public Pair(int a, int b) {
            this.a = a;
            this.b = b;
        }
        //        to sort first part
//        public int compareTo(Pair other) {
//            if (this.a == other.a) return other.b > this.b ? -1 : 1;
//            else if (this.a > other.a) return 1;
//            else return -1;
//        }
//        public int compareTo(Pair other) {
//            if (this.b == other.b) return 0;
//            if (this.b < other.b) return 1;
//            else return -1;
//        }
        //sort on the basis of first part only
        public int compareTo(Pair other) {
            if (this.a == other.a) return 0;
            else if (this.a > other.a) return 1;
            else return -1;
        }

    }
    static int[] frequency(String s){
        int fre[]= new int[26];
        for (int i=0;i<s.length();i++){
            fre[s.charAt(i)-'a']++;
        }
        return fre;
    }
    static long LOWERBOUND(long a[],long k){
        int s=0,e=a.length-1;
        long ans=-1;
        while (s<=e){
            int mid=(s+e)/2;
            if (a[mid]<=k){
                ans=mid;
                s=mid+1;
            }
            else {
                e=mid-1;
            }
        }
        return ans;
    }
    static int mod =(int)(1e9+7);
    static long mod(long x) {
        return ((x % mod + mod) % mod);
    }
    static long add(long x, long y) {
        return mod(mod(x) + mod(y));
    }
    static long mul(long x, long y) {
        return mod(mod(x) * mod(y));
    }
    //Fast Power(logN)
    static int fastPower(long a,long n){
        int ans=1;
        while (n>0){
            long lastBit=n&1;
            if (lastBit==1){
                ans=(int)mul(ans,a);
            }

            a=(int)mul(a,a);
            n>>=1;
        }
        return ans;
    }
    static int[] find(int n, int start, int diff) {
        int a[] = new int[n];
        a[0] = start;
        for (int i = 1; i < n; i++) a[i] = a[i - 1] + diff;
        return a;
    }
    static void swap(int a, int b) {
        int c = a;
        a = b;
        b = c;
    }
    static void printArray(int a[]) {
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
    }
    static boolean sorted(int a[]) {
        int n = a.length;
        boolean flag = true;
        for (int i = 0; i < n - 1; i++) {
            if (a[i] > a[i + 1]) flag = false;
        }
        if (flag) return true;
        else return false;
    }
    public static int findlog(long n) {
        if (n == 0)
            return 0;

        if (n == 1)
            return 0;
        if (n == 2)
            return 1;
        double num = Math.log(n);
        double den = Math.log(2);
        if (den == 0)
            return 0;
        return (int) (num / den);
    }
    public static long gcd(long a, long b) {
        if (b % a == 0)
            return a;
        return gcd(b % a, a);
    }
    public static int gcdInt(int a, int b) {

        if (b % a == 0)
            return a;

        return gcdInt(b % a, a);

    }
    static void sortReverse(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) l.add(i);
        //        Collections.sort.(l);
        Collections.sort(l, Collections.reverseOrder());
        for (int i = 0; i < a.length; i++) a[i] = l.get(i);
    }
    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        String next() {
            while (!st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        long[] readArrayLong(long n) {
            long[] a = new long[(int) n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }
    }
}