Problem: It is the hard version of the problem. The only difference is that in this version 3 ≤ k ≤ n.

You are given a positive integer n. Find k positive integers a_1, a_2, …, a_k, such that:

  * a_1 + a_2 + … + a_k = n 
  * LCM(a_1, a_2, …, a_k) ≤ n/2 



Here LCM is the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of numbers a_1, a_2, …, a_k.

We can show that for given constraints the answer always exists.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The only line of each test case contains two integers n, k (3 ≤ n ≤ 10^9, 3 ≤ k ≤ n).

It is guaranteed that the sum of k over all test cases does not exceed 10^5.

Output

For each test case print k positive integers a_1, a_2, …, a_k, for which all conditions are satisfied.

Example

Input


2
6 4
9 5


Output


1 2 2 1 
1 3 3 1 1 

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 C
{
    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 long a[];
    static long dp[][];

    public static long dp(int i, int j){
        // prln(Arrays.toString(a)+" "+i+", "+j);
        if(i == j) return 0;
        if(dp[i][j] != -1L) return dp[i][j];
        dp[i][j] = (a[j] - a[i]) + min(dp(i+1,j), dp(i,j-1));
        return dp[i][j];
    }

    // 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 k = in();
            if(k == 3){
                ifK3(n);
            }
            else{
                int x = k - 3;
                for(int i = 0 ;i < x; i++){
                    app(1+" ");

                }
                ifK3(n-x);
            }
        }
        out.printLine(sb);
        out.close();
    }

    public static void ifK3(int n){
        if(n % 2 != 0){
            app(1+" "+(n/2)+" "+(n/2)+"\n");
        }
        else if(n == 4){
            app(2+" "+1+" "+1+"\n");
        }
        else if((n/2) % 2 != 0){
            app(2+" "+((n-2)/2)+" "+((n-2)/2)+"\n");
        }
        else{
            int x = n / 2;
            int y = x / 2;
            app(x+" "+y+" "+y+"\n");
        }
    }

    static class Pair{

        int index;
        int height;

        public Pair(int index, int height){
            this.index = index;
            this.height = height;
        }

        public String toString(){
            return "[ "+index+" , "+height+" ]";
        }
    }

    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();
        }
    }
}