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 java.awt.image.AreaAveragingScaleFilter;
import java.io.*;
import java.util.*;
//_________________________________________________________________
public class Main {
    static int remove(int a[] ,int n){
        if (n==0||n==1)return n;
        int j=0;
        sort(a);
        for (int i=0;i<n-1;i++){
            if (a[i]!=a[i+1]){
                a[j]=a[i];
                j++;
            }
        }
        a[j++]=a[n-1];
        return j;
    }
    public static int countKdivPairs(int A[], int n, int K)
    {
        // Create a frequency array to count
        // occurrences of all remainders when
        // divided by K
        int freq[] = new int[K];

        // Count occurrences of all remainders
        for (int i = 0; i < n; i++)
            ++freq[A[i] % K];

        // If both pairs are divisible by 'K'
        int sum = freq[0] * (freq[0] - 1) / 2;

        // count for all i and (k-i)
        // freq pairs
        for (int i = 1; i <= K / 2 && i != (K - i); i++)
            sum += freq[i] * freq[K - i];
        // If K is even
        if (K % 2 == 0)
            sum += (freq[K / 2] * (freq[K / 2] - 1) / 2);
        return sum;
    }
    public static void main(String[] args) throws IOException {
//        File file = new File("input.txt");
        FastScanner sc = new FastScanner();
//                Scanner sc= new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t=sc.nextInt();
        int x=1;
        while (t-->=1) {
            int n = sc.nextInt(),k=sc.nextInt();
            for (int i=0;i<k-3;i++){
                System.out.print(1+" ");
            }
            n=n-(k-3);
            if (n%2!=0){
                System.out.print(1+" "+(n/2)+" "+n/2);
            }
            else{
                if ((n/2)%2==0){
                    System.out.print(n/2+" "+(n/4)+" "+(n/4));
                }
                else{
                    System.out.print(2+" "+(n-2)/2+" "+(n-2)/2);
                }
            }
            System.out.println();






        }
        out.flush();
    }
    //------------------------------------if-------------------------------------------------------------------------------------------------------------------------------------------------
    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 int mod =(int)1e9;
    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));
    }
    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());
        }
    }
}