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.io.*;
import java.math.*;
import java.security.*;
import java.text.*;
import java.util.*;
import java.util.concurrent.*;
import java.util.function.*;
import java.util.regex.*;
import java.util.stream.*;
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toList;




public class Main{

    static long MOD = 1_000_000_007L;
    //static long MOD = 998_244_353L;
    //static long MOD = 1_000_000_033L;
    static long inv2 = (MOD + 1) / 2;
    static long [] fac;
    static long [] pow;
    static long [] inv;
    static int[][] dir = new int[][]{{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
    static long lMax = 0x3f3f3f3f3f3f3f3fL;
    static int iMax = 0x3f3f3f3f;
    static HashMap <Long, Long> memo = new HashMap();
    static MyScanner sc = new MyScanner();
    //static ArrayList <Integer> primes;

    static long[] pow2;
    static int[] base;
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
    public static void main(String[] args) {
        out = new PrintWriter(new BufferedOutputStream(System.out));
        // Start writing your solution here. -------------------------------------

        int nn = 300000;

        /*fac = new long[nn + 1];
        fac[1] = 1;
        for(int i = 2; i <= nn; i++)
            fac[i] = fac[i - 1] * 1L * i % MOD;*/

        /*pow = new long[nn + 1];
        pow[0] = 1L;
        for(int i = 1; i <= nn; i++)
            pow[i] = pow[i - 1] * 2L % MOD;
        pow[1] = 3L;*/

        /*pow2 = new long[nn + 1];
        pow2[0] = 1L;
        for(int i = 1; i <= nn; i++)
            pow2[i] = pow2[i - 1] * 2L % (MOD - 1);*/

        /*inv = new long[nn + 1];
        inv[1] = 1;
        for (int i = 2; i <= nn; ++i)
            inv[i] = (MOD - MOD / i) * inv[(int)(MOD % i)] % MOD;*/

        //primes = sieveOfEratosthenes(100001);

        int t = 1;
        t = sc.ni();
        /*
        base = new int[10000001]
        Arrays.fill(base, -1);
        for(int i = 1; i <= 10000000; i++) {
            int j = 1, tmp = i;
            while(true) {
                tmp = j * j * i;
                if(tmp > 10000000) break;
                if(base[tmp] == -1) base[tmp] = i;
                j ++;
            }
        }*/
        while(t-- > 0) {
            Object res = solve();
            //out.println(res);
        }
        out.close();
    }


    static Object solve() {
        /*String s = sc.nextLine();
        char[] c = s.toCharArray();
        int n = c.length;*/
        //int n = sc.ni();
        //long[] a =  new long[n];
        //for(int i = 0; i < n; i++) a[i] = sc.nl();
        int n = sc.ni(), k = sc.ni(), res = 0;
        int[] a = new int[k];
        if(k == 3) return solve3(n, k);
        ArrayList <Integer> ans = new ArrayList<>();
        while(k >= 8) {
            for(int i = 0; i < 4; i++)
                ans.add(1);
            n -= 4;
            k -= 4;
        }
        if(k == 4 && n % 4 == 3) {
            ans.add(2);
            ans.add(1);
            ans.add(n / 2 - 1);
            ans.add(n / 2 - 1);
        } else {
            if(k == 4 && (n % 4 == 1 || n % 4 == 2)) {
                int base = n / 4;
                ans.add(base);
                ans.add(base);
                ans.add(base * 2);
                ans.add(n % 4);
            } else if(k == 5 && (n % 4 == 3 || n % 4 == 0)) {
                int base = (n - 1) / 4;
                ans.add(base);
                ans.add(base);
                ans.add(base * 2);
                ans.add(2);
                ans.add((n - 2) % 4);
            } else if(k == 6 && (n % 4 == 1 || n % 4 == 2)) {
                int base = n / 4 - 1;
                ans.add(base);
                ans.add(base);
                ans.add(base * 2);
                ans.add(2);
                ans.add(2);
                ans.add(n % 4);
            } else {
                int base = n / 4;
                if(4 * base + k - 4 > n) base--;
                for(int i = 0; i < 4; i++) ans.add(base);
                n -= 4 * base;
                while(n > 0) {
                    int adding = Math.min(n / (k - 4), 2);
                    n -= adding;
                    k--;
                    ans.add(adding);
                }
            }
        }
        for(int i : ans) out.print(i + " ");
        out.println();
        return res + 1;
    }

    static Object solve3(int n, int k) {
        /*String s = sc.nextLine();
        char[] c = s.toCharArray();
        int n = c.length;*/
        //int n = sc.ni();
        //long[] a =  new long[n];
        //for(int i = 0; i < n; i++) a[i] = sc.nl();
        int res = 0;
        int[] a;
        if(n % 2 == 1) a = new int[]{n / 2, n / 2, 1};
        else if(n % 4 == 0) a = new int[]{n / 2, n / 4, n / 4};
        else a = new int[]{2, n / 2 - 1, n / 2 - 1};
        out.println(a[0] + " " + a[1] + " " + a[2]);
        return res;
    }



    // SegmentTree range min/max query From uwi
    public static class SegmentTreeRMQ {
        public int M, H, N;
        public int[] st;

        public SegmentTreeRMQ(int n)
        {
            N = n;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            Arrays.fill(st, 0, M, Integer.MAX_VALUE);
        }

        public SegmentTreeRMQ(int[] a)
        {
            N = a.length;
            M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
            H = M>>>1;
            st = new int[M];
            for(int i = 0;i < N;i++){
                st[H+i] = a[i];
            }
            Arrays.fill(st, H+N, M, Integer.MAX_VALUE);
            for(int i = H-1;i >= 1;i--)propagate(i);
        }

        public void update(int pos, int x)
        {
            st[H+pos] = x;
            for(int i = (H+pos)>>>1;i >= 1;i >>>= 1)propagate(i);
        }

        private void propagate(int i)
        {
            st[i] = Math.min(st[2*i], st[2*i+1]);
        }

        public int minx(int l, int r){
            int min = Integer.MAX_VALUE;
            if(l >= r)return min;
            while(l != 0){
                int f = l&-l;
                if(l+f > r)break;
                int v = st[(H+l)/f];
                if(v < min)min = v;
                l += f;
            }

            while(l < r){
                int f = r&-r;
                int v = st[(H+r)/f-1];
                if(v < min)min = v;
                r -= f;
            }
            return min;
        }

        public int min(int l, int r){ return l >= r ? 0 : min(l, r, 0, H, 1);}

        private int min(int l, int r, int cl, int cr, int cur)
        {
            if(l <= cl && cr <= r){
                return st[cur];
            }else{
                int mid = cl+cr>>>1;
                int ret = Integer.MAX_VALUE;
                if(cl < r && l < mid){
                    ret = Math.min(ret, min(l, r, cl, mid, 2*cur));
                }
                if(mid < r && l < cr){
                    ret = Math.min(ret, min(l, r, mid, cr, 2*cur+1));
                }
                return ret;
            }
        }
    }

    public static char[] rev(char[] a){char[] b = new char[a.length];for(int i = 0;i < a.length;i++)b[a.length-1-i] = a[i];return b;}

    public static double dist(double a, double b){
        return Math.sqrt(a * a + b * b);
    }

    public static long inv(long a){
        return quickPOW(a, MOD - 2);
    }

    public class Interval {
        int start;
        int end;
        public Interval(int start, int end) {
            this.start = start;
            this.end = end;
        }
    }

    public static ArrayList<Integer> sieveOfEratosthenes(int n) {
        boolean prime[] = new boolean[n + 1];
        Arrays.fill(prime, true);
        for (int p = 2; p * p <= n; p++) {
            if (prime[p]) {
                for (int i = p * 2; i <= n; i += p) {
                    prime[i] = false;
                }
            }
        }
        ArrayList<Integer> primeNumbers = new ArrayList<>();
        for (int i = 2; i <= n; i++) {
            if (prime[i]) {
                primeNumbers.add(i);
            }
        }
        return primeNumbers;
    }


    public static int lowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
    public static int lowerBound(int[] a, int l, int r, int v)
    {
        if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
        int low = l-1, high = r;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] >= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }
    public static int rlowerBound(int[] a, int v){ return lowerBound(a, 0, a.length, v); }
    public static int rlowerBound(int[] a, int l, int r, int v)
    {
        if(l > r || l < 0 || r > a.length)throw new IllegalArgumentException();
        int low = l-1, high = r;
        while(high-low > 1){
            int h = high+low>>>1;
            if(a[h] <= v){
                high = h;
            }else{
                low = h;
            }
        }
        return high;
    }
    public static long C(int n, int m)
    {
        if(m == 0 || m == n) return 1l;
        if(m > n || m < 0) return 0l;
        long res = fac[n] * quickPOW((fac[m] * fac[n - m]) % MOD, MOD - 2) % MOD;

        return res;
    }
    public static long quickPOW(long n, long m)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % MOD;
            n = (n * n) % MOD;
            m >>= 1;
        }
        return ans;
    }
    public static long quickPOW(long n, long m, long mod)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % mod;
            n = (n * n) % mod;
            m >>= 1;
        }
        return ans;
    }

    public static int gcd(int a, int b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }
    public static long gcd(long a, long b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }

    static class Randomized {
        public static void shuffle(int[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(int[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                int tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static void shuffle(long[] data) {
            shuffle(data, 0, data.length - 1);
        }

        public static void shuffle(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return RandomWrapper.INSTANCE.nextInt(l, r);
        }
    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper(new Random());

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }


    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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 ni() {
            return Integer.parseInt(next());
        }
        long nl() {
            return Long.parseLong(next());
        }
        double nd() {
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}