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.util.*;
import java.io.*;
import java.lang.Math;
// boomer boomer


public class A {

    static int INF = -2_000_000_000;
    static long MOD = 1_000_000_007;
    static int MAX_PRIME = 1_000_000_000;
    public static void main(String args[]) {
        FastScanner fs=new FastScanner();
        int T = fs.nextInt();
outer: for(int tt=0; tt < T; tt++) {
			int N = fs.nextInt(), M = fs.nextInt();
            TreeSet<Integer> ts=new TreeSet<>();
            int A[] = new int[N];
            
            for(int i =0; i < N; i++) A[i] = fs.nextInt();
            int s = 0;
            for(int i : A) s += i;
            if(s == M) {
                System.out.println("NO");
                continue outer;
            }
            for(int i : A) ts.add(i);
            ArrayDeque<Integer> ans=new ArrayDeque<>();
            for(int i = 0; i < N; i++) {
                int t = ts.first();
                if(M - t == 0) {
                    int p = ts.last();
                    if(p == t) {
                        System.out.println("NO");
                        continue outer;
                    } else {
                        M -= p;
                        ts.remove(p);
                        ans.add(p);
                    }
                } else {
                    M -= t;
                    ans.add(t);
                    ts.remove(ts.first());
                }
            }
            System.out.println("YES");
            for(int i : ans) {
                System.out.print(i + " ");
            }
            System.out.println();
        }
    }

    static boolean isprime(long X) {
        return miller_rabin(X);
    }

    static long modmul(long a, long b, long M) {
        long ret = a * b - M * (long)(1.0 / M * a * b);
        return ret + M * (ret < 0 ? 1 : 0) - M * (ret >= (long)M ? 1 : 0);
    }
    static boolean miller_rabin(long n) {
        if(n < 2 || n % 6 % 4 != 1 ) return (n | 1) == 3;

        long nums[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
        long s = Long.numberOfTrailingZeros(n - 1), d = n >> s;
        for(long a : nums) {
            long p = modpow(a%n, d, n), i = s;
            while(p != 1 && p != n - 1 && (a%n!=0) && (i-- != 0)) {
                p = modmul(p, p, n);
            }

            if(p != n-1 && i != s) return false;
        }
        return true;
    }
    static long modpow(long x, long y, long MOD) {
        if(y == 0)
            return 1;

        long mid = modpow(x, y/2, MOD);
        if((y&1)==1) {
            return (((mid*mid)%MOD)*x)%MOD;
        } else {
            return (mid*mid)%MOD;
        }
    }

    static boolean perfectSquare(int x) {
        return (int)Math.sqrt(x) * (int)Math.sqrt(x) == x;
    }






    static class Pair implements Comparable<Pair>{
        long first, second;
        public Pair(long l, long i) {
            first=l;second=i;
        }
        public Pair() {
            first=0;second=0;
        }
        public int compareTo(Pair x) {
            if(this.first<x.first)
                return -1;
            if(this.first==x.first)
                return this.second<x.second?-1:(this.second==x.second?0:1);
            return 1;
        }
    }



    static class RangeMin {
        long logs[], st[][];
        // sparse table?
        int N, K;
        public RangeMin(int n) {
            N=n;
            K = (int)((double) (Math.log10((double)n) /(double) Math.log10((double)2) ));
            st = new long [N+2][K+2];
            logs = new long[N+2];
        }
        void init(ArrayList<Integer> A) {

            for(int i = 0; i < N; i++) {
                Arrays.fill(st[i], (long)1e18);
                st[i][0]=(long)A.get(i);
            }
            // NLOGN
            for(int j = 1; j <= K; j++) {
                for(int i = 0; i + (1<<j) <= N; i++) {
                    st[i][j]=Math.min(st[i][j-1], st[i + (1 << (j-1))][j-1]);
                }
            }
            logs[1]=0;
            for(int i = 2; i <= N; i++) {
                logs[i]=logs[i/2]+1;
            }
        }
        void init(int [] A) {

            for(int i = 0; i < N; i++) {
                Arrays.fill(st[i], (long)1e18);
                st[i][0]=(long)A[i];
            }
            // NLOGN
            for(int j = 1; j <= K; j++) {
                for(int i = 0; i + (1<<j) <= N; i++) {
                    st[i][j]=Math.min(st[i][j-1], st[i + (1 << (j-1))][j-1]);
                }
            }
            logs[1]=0;
            for(int i = 2; i <= N; i++) {
                logs[i]=logs[i/2]+1;
            }
        }

        long query(int L, int R) {
            int j = (int)logs[R-L+1];
            return Math.min(st[L][j], st[R - (1 << j) + 1][j]);
        }
    }

    static class FastScanner 
    { 
        BufferedReader br; 
        StringTokenizer st; 

        public FastScanner() 
        { 
            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 nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 

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

        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 

        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        }
        public int[] nextArray(int n) {
            int a[] = new int[n];
            for(int i =0; i < n; i++) a[i]=this.nextInt();
            return a;
        }
        public int max(int a[]) {
            int mx = Integer.MIN_VALUE;
            for(int i : a)
                mx = Math.max(i, mx);
            return mx;
        }
        public int count(int a[], int val) {
            int ans =0;
            for(int i : a)
                ans += val == i ? 1 : 0;
            return ans;
        }
        public int min(int a[]) {
            int mn = Integer.MAX_VALUE;
            for(int i : a)
                mn = Math.min(i, mn);
            return mn;
        }
        public void randomShuffleSort(int []a) {
            Random r = new Random();
            for(int i =0; i < (a.length)/2; i++) {
                int temp=a[i],p=r.nextInt(a.length);
                a[i]=a[p];
                a[p]=temp;
            }
            this.fine_sort(a);
        }
        public void fine_sort(int a[]) {
            ArrayList<Integer> A = new ArrayList<>();
            for(int i : a) A.add(i);
            Collections.sort(A);
            for(int i=0; i < a.length; i++) {
                a[i]=A.get(i);
            }
        } 
    }
    static class SegTree {
        int SIZE;
        // change to longs sirs
        int array[];
        int vals[];
        int lazy[];
        SegTree(int a[]) {
            int S = a.length;
            SIZE = 1;
            while(SIZE < S) SIZE *= 2;
            array = new int[2 * SIZE];
        }

        void build(int rt, int v1, int v2) {

        }
    }
    static class SegmentTree {
        int leftmost, rightmost;
        SegmentTree lChild, rChild;
        int sum;
        long lz_val;

        public SegmentTree(int l, int r, int a[]) {
            leftmost = l;
            rightmost = r;
            lz_val=0;
            if(l == r)
                sum = a[l];
            else {
                int mid = (l + r) / 2;
                lChild = new SegmentTree(l, mid, a);
                rChild = new SegmentTree(mid+1, r, a);
                update();
            }
        }
        public void update() {
            sum = lChild.sum + rChild.sum + (int)lChild.lz_val + (int)rChild.lz_val;
        }
        public void pointUpdate(int pos, int val) {
            if(leftmost == rightmost) {
                sum = val;
            } else {
                int mid = (leftmost + rightmost) / 2;
                if(pos <= lChild.rightmost) lChild.pointUpdate(pos, val);
                else rChild.pointUpdate(pos, val);
                update();
            }
        }
        public void rangeUpdate(int l, int r, int val) {
            // first check if it's within the range
            if(l <= leftmost && r >= rightmost) {
                lz_val += val;
            } else {
                // its not within the range so lets update the left if we have to and update the right if we have to
                if(lChild.rightmost >= l) lChild.rangeUpdate(l, r, val);
                if(rChild.leftmost <= r) rChild.rangeUpdate(l, r, val);
                update();
            }
        }
        public long query(int l, int r) {
            if(l > rightmost || r < leftmost) return 0;
            else if(l <= leftmost && r >= rightmost) return sum + lz_val;

            return (long) lChild.query(l, r) + (long) rChild.query(l, r);
        }
    }
}