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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.List;
import java.util.NoSuchElementException;

public class Main {

	/* PriorityQueueは拡張for文で出すとsortされてない順番で出てくる
	 * longのbit演算は1L<<posに注意
	 * JOIはMLEが厳しい。最悪shortを使う。ArrayListはオートボクシングが遅いから、自作listが早い
	 */

	/*略語
	 * 2-to, 4-for, 8-from
	 * -L -long(型), -P -素数Pを法とした余り
	 * a,b -任意の引数, n,m -自然数, p -素数
	 * pos -postition
	 * abs -絶対値
	 * min -minimum, max -maximum, ave -average
	 * div -divide
	 * pow -power(累乗)
	 * ceil -ceiling(天井関数)
	 * dt -data
	 * ln -length
	 * sc -scanner
	 * INF -INFINITY
	 * e97 -10E9+7=1000000007(よく使われる素数)
	 */

	public static void main(String[] args) throws Exception {

		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);


		int Q = sc.nexI();

		for(int t=0; t<Q; t++) {
			/*int n = sc.nexI();
			int m = sc.nexI();
			int[] as = new int[n];
			sc.ai(as);
			
			int[] modM = new int[m];
			
			for(int e:as) {
				modM[e%m]++;
			}
			
			int ans=0;
			
			if(modM[0]>0) ans++;
			
			for(int i=1; i<((m+1)/2); i++) {
				int d = abs(modM[i]-modM[m-i]);
				if(d==0) d++;
				ans+=d;
			}
			if(m%2==0) {
				if(modM[m/2]>0) ans++;
			}
			out.println(ans);*/

			int n = sc.nexI();
			int k = sc.nexI();
			
			for(int i=0; i<(k-3); i++) {
				out.print("1 ");
				n--;
			}
			
			if(n%4==0) {
				out.println((n/4)+" "+(n/4)+" "+(n/2));
			}else if(n%2==0){
				n -=2;
				n/=2;
				out.println("2 "+n+" "+n);
			}else{
				n -=1;
				n/=2;
				out.println("1 "+n+" "+n);
			}
		}
		
		
		out.flush();
		return;
	}
	private static int INF = (int) 1e8;
	private static long INFL = (long) 1e17;
	private static long e97 = 1000000007L;
	private static long e99 =  998244353L;

	private static void assertion(boolean should_true) {
		//should_trueがtrueでなければエラーを起こす。「断言」
		if(!should_true) throw new AssertionError();
	}

	private static int abs(int a) {
		return (a>=0) ? a: -a;
	}
	private static long abs(long a) {
		return (a>=0) ? a: -a;
	}
	private static double abs(double a) {
		return (a>=0.0) ? a: -a;
	}

	private static int min(int a, int b) {
		return (a>b) ? b : a;
	}
	private static long min(long a, long b) {
		return (a>b) ? b : a;
	}
	private static double min(double a, double b) {
		return (a>b) ? b : a;
	}

	private static int max(int a, int b) {
		return (a>b) ? a : b;
	}
	private static long max(long a, long b) {
		return (a>b) ? a : b;
	}
	private static double max(double a, double b) {
		return (a>b) ? a : b;
	}


	private static int pow2(int num2pow) {
		return num2pow*num2pow;
	}
	private static long pow2(long num2pow) {
		return num2pow*num2pow;
	}


	private static int pow(int num_powered, int index) {
		int ans = 1;
		for(int i=0; i<index; i++) {
			ans *= num_powered;
			assertion(ans>=0);
		}
		return ans;
	}
	private static long pow(long num_powered, int index) {
		long ans = 1L;
		for(int i=0; i<index; i++) {
			ans *= num_powered;
			assertion(ans>=0L);
		}
		return ans;
	}
	private static long powP(long num_powered, long index, long p) {
		//繰り返し二乗法
		if(num_powered==0L) return 0L;
		if(index==0L) return 1L;
		if(index==2L) {
			long ans = num_powered*num_powered;
			assertion(ans>0);
			return ans%p;
		}

		int d = getDigit2(index);

		long next = 0L;
		long[] num_done_by2 = new long[d+1];
		num_done_by2[0] = num_powered;
		for(int i=1; i<=d; i++) {
			next = num_done_by2[i-1]*num_done_by2[i-1];
			assertion(next>0);
			num_done_by2[i] = next%p;
		}
		long ans=1L;
		for(int i=d; i>=0; i--) {
			if(index >= (1L<<(long)i)) {
				index -= (1L<<(long)i);
				ans = ans*num_done_by2[i];
				assertion(ans>0);
				ans %= p;
			}
 		}
		return ans%p;
	}
	private static double hypod(double a, double b) {
		return Math.sqrt(a*a+b*b);
	}

	private static int getDigit2(long num2know) {
		long compare4 = 1L;
		int digit = 0;
		while(num2know > compare4) {
			digit ++;
			compare4 = (1L<<(long)digit);
		}
		return digit; //numは2^d以下
	}
	private static int getDigit10(long num2know) {
		long compare4 = 1L;
		int digit = 0;
		while(num2know >= compare4) {
			digit ++;
			compare4 *= 10L;
		}
		return digit; //numはd桁の数で、10^dより小さい

	}


	private static int divceil(int numerator, int denominator) {
		return (numerator+denominator-1)/denominator;
	}
	private static long divceil(long numerator, long denominator) {
		return (numerator+denominator-1L)/denominator;
	}


	private static long factorial(int n) {
		long ans=1L;
		for(long i=n; i>0; i--) {
			ans *= i;
			assertion(ans>=0L);
		}
		return ans;
	}
	private static long facP(int n, long p) {
		long ans=1L;
		for(long i=n; i>0; i--) {
			ans *= i;
			ans %= p;
		}
		return ans;
	}

	private static long lcm(long m, long n) {
		assertion((m>0L) && (n>0L));
		long ans = m/gcd(m,n);
		ans *= n;
		return ans;
	}
	private static long gcd(long m, long n) {
		//if(isINFL(-m)) return n;
		assertion((m>=0L) && (n>=0L));
		if(m < n) return gcd(n, m);
		if(n == 0) return m;
		return gcd(n, m % n);
	}

	private static boolean is_prime(long n2check) {
		if(n2check==1L) return false;
		for(long i=2L; i<=Math.sqrt(n2check); i++) {
			if(n2check%i == 0) return false;
		}
		return true;
	}

	private static long modinv(long n, long p) {
		assertion((n>0L)&&(p>1L)&&(gcd(n,p)==1L));
		//a⊥p, >1に注意
		n %= p;

		//yn≡1(mod p)
		//<-> xp+yn=1;	(n<p)
		//...(sx+ty)a+(ux+vy)b=1	(|sv-tu|=1)
		//...(sx+ty)a+(ux+vy)=1
		//<- sx+ty=0, ux+vy=1

		long a=p, b=n, s=1, t=0, u=0, v=1;
		while(b>1) {
			long quo = a/b;
			long rem = a%b;
			a=b; b=rem;
			long s2 = s*quo+u, t2=t*quo+v;
			u=s; v=t;
			s=s2; t=t2;
		}
		long det = s*v-t*u;
		assertion(abs(det)==1);
		s /= det;

		/*long b = p, u = 1L, v = 0L;//動作原理不明
		while (b > 0) {
			long t = a / b;
			long pe = a%b;
			a = b;
			b = pe;
			pe = u-t*v;
			u = v;
			v = pe;
		}*/
		s %= p;
		if(s < 0L) s += p;
		return s;
	}

	private static int minAll(int[] dt4min) {
		int min = INF;
		for(int i=0; i<dt4min.length; i++) {
			if(dt4min[i] < min) min = dt4min[i];
		}
		return min;
	}
	private static long minAll(long[] dt4min) {
		long min = INFL;
		for(int i=0; i<dt4min.length; i++) {
			if(dt4min[i] < min) min = dt4min[i];
		}
		return min;
	}
	private static int maxAll(int[] dt4max) {
		int max = -INF;
		for(int i=0; i<dt4max.length; i++) {
			if(dt4max[i] < max) max = dt4max[i];
		}
		return max;
	}
	private static long maxAll(long[] dt4max) {
		long max = -INFL;
		for(int i=0; i<dt4max.length; i++) {
			if(dt4max[i] < max) max = dt4max[i];
		}
		return max;
	}

	private static int sumAll(int[] dt4sum) {
		int sum_of_dt = 0;
		for(int element: dt4sum) {
			sum_of_dt += element;
		}
		return sum_of_dt;
	}
	private static long sumAll(long[] dt4sum) {
		long sum_of_dt = 0L;
		for(long element: dt4sum) {
			sum_of_dt += element;
		}
		return sum_of_dt;
	}
	private static int sumAll(ArrayList<Integer> dt4sum) {
		int sum_of_dt = 0;
		for(long element: dt4sum) {
			sum_of_dt += element;
		}
		return sum_of_dt;
	}
	/*private static long sumAll(ArrayList<Long> dt4sum) {
		long sum_of_dt = 0L;
		for(long element: dt4sum) {
			sum_of_dt += element;
		}
		return sum_of_dt;
	}*/

	private static int[] reverse(int[] as) {
		int ln = as.length;
		int[] bs = new int[ln];
		for(int i=0; i<ln; i++) {
			bs[i] = as[ln-i-1];
		}
		return bs;
	}


	private static boolean is_in_area(int y, int x, int height, int width) {
		if(y < 0) return false;
		if(x < 0) return false;
		if(y >= height) return false;
		if(x >= width) return false;
		return true;
	}

	private static boolean is_in_area(Vector v, int height, int width) {
		if(v.y < 0) return false;
		if(v.x < 0) return false;
		if(v.y >= height) return false;
		if(v.x >= width) return false;
		return true;
	}


	private static int nC2(int n) {
		return ((n*(n-1))/2);
	}
	private static long nC2(long n) {
		return ((n*(n-1L))/2L);
	}


	private static int iflag(int pos) {
		assertion(pos<31);
		return (1<<pos);
	}
	private static long flag(int pos) {
		assertion(pos<63);
		return (1L<<(long)pos);
	}
	private static boolean isFlaged(int bit, int pos) {
		if((bit&(1<<pos)) > 0) return true;
		else return false;
	}
	private static boolean isFlaged(long bit, int pos) {
		if((bit&(1L<<(long)pos)) > 0L) return true;
		else return false;
	}
	private static int deflag(int bit, int pos) {
		return bit&~(1<<pos);
	}
	private static int countFlaged(int bit) {
		int ans=0;
		for(int i=0; i<31; i++) {
			if((bit&(1<<i)) > 0) ans++;
		}
		return ans;
	}
	private static int countFlaged(long bit) {
		int ans=0;
		for(long i=0; i<63L; i++) {
			if((bit&(1L<<i)) > 0) ans++;
		}
		return ans;
	}

	private static int[] Xdir4 = {1,0,0,-1};
	private static int[] Ydir4 = {0,1,-1,0};
	private static int[] Xdir8 = {1,1,1,0,0,-1,-1,-1};
	private static int[] Ydir8 = {1,0,-1,1,-1,1,0,-1};

	public static int biSearch(int[] dt, int target) {
		int left=0, right=dt.length-1;
		int mid=-1;
		while(left<=right) {
			mid = (right+left)/2;
			if(dt[mid] == target) return mid;
			if(dt[mid] < target) left=mid+1;
			else right=mid-1;
		}
		return -1;
	}

	public static int biSearchMax(long[] dt, long target) {
		int left=-1, right=dt.length, mid=-1;
		while((right-left)>1) {
			mid = (right+left)/2;
			if(dt[mid] < target) left=mid;
			else right=mid;
		}
		return left;	//target未満の最大のaddress
	}
	public static int biSearchMin(long[] dt, long target) {
		int left=-1, right=dt.length, mid=-1;
		while((right-left)>1) {
			mid = (right+left)/2;
			if(dt[mid] <= target) left=mid;
			else right=mid;
		}
		return right;	//targetより大きい最小のaddress
	}

	private static void fill(boolean[] target, boolean reset) {
		for(int i=0; i<target.length; i++) {
			target[i] = reset;
		}
	}
	private static void fill(int[] target, int reset) {
		for(int i=0; i<target.length; i++) {
			target[i] = reset;
		}
	}
	private static void fill(long[] target, long reset) {
		for(int i=0; i<target.length; i++) {
			target[i] = reset;
		}
	}
	private static void fill(char[] target, char reset) {
		for(int i=0; i<target.length; i++) {
			target[i] = reset;
		}
	}
	private static void fill(double[] target, double reset) {
		for(int i=0; i<target.length; i++) {
			target[i] = reset;
		}
	}

	private static void fill(boolean[][] target,boolean reset) {
		for(int i=0;i<target.length; i++) {
			for(int j=0; j<target[i].length; j++) {
				target[i][j] = reset;
			}
		}
	}
	private static void fill(int[][] target, int reset) {
		for(int i=0; i<target.length; i++) {
			for(int j=0; j<target[i].length; j++) {
				target[i][j] = reset;
			}
		}
	}
	private static void fill(long[][] target, long reset) {
		for(int i=0; i<target.length; i++) {
			for(int j=0; j<target[i].length; j++) {
				target[i][j] = reset;
			}
		}
	}
	private static void fill(char[][] target, char reset) {
		for(int i=0; i<target.length; i++) {
			for(int j=0; j<target[i].length; j++) {
				target[i][j] = reset;
			}
		}
	}
	private static void fill(double[][] target, double reset) {
		for(int i=0; i<target.length; i++) {
			for(int j=0; j<target[i].length; j++) {
				target[i][j] = reset;
			}
		}
	}
	private static void fill(int[][][] target,int reset) {
		for(int i=0;i<target.length;i++) {
			for(int j=0;j<target[i].length;j++) {
				for(int k=0;k<target[i][j].length;k++) {
					target[i][j][k]=reset;
				}
			}
		}
	}
	private static void fill(long[][][] target,long reset) {
		for(int i=0;i<target.length;i++) {
			for(int j=0;j<target[i].length;j++) {
				for(int k=0;k<target[i][j].length;k++) {
					target[i][j][k]=reset;
				}
			}
		}
	}

	private static void showBit(int bit) {
		for(int i=0; i<getDigit2(bit); i++) {
			if(isFlaged(bit,i)) System.out.print("O");
			else System.out.print(".");
		}
		System.out.println();
	}
	private static void showBit(long bit) {
		for(int i=0; i<getDigit2(bit); i++) {
			if(isFlaged(bit,i)) System.out.print("O");
			else System.out.print(".");
		}
		System.out.println();
	}
	static void show2(boolean[][] dt, String cmnt) {
		for(int i=0; i<dt.length; i++) {
			for(int j=0; j<dt[i].length; j++) {
				if(dt[i][j]) System.out.print("O");
				else System.out.print(".");
			}
			if(!cmnt.equals("")) System.out.print("<-"+cmnt);
			System.out.println(" :"+i);
		}
	}
	static void show2(int[][] dt, String cmnt) {
		for(int i=0; i<dt.length; i++) {
			for(int j=0; j<dt[i].length; j++) {
				System.out.print(dt[i][j]+",");
			}
			if(!cmnt.equals("")) System.out.print("<-"+cmnt);
			System.out.println(" :"+i);
		}
	}
	static void show2(long[][] dt, String cmnt) {
		for(int i=0; i<dt.length; i++) {
			for(int j=0; j<dt[i].length; j++) {
				System.out.print(dt[i][j]+",");
			}
			if(!cmnt.equals("")) System.out.print("<-"+cmnt);
			System.out.println(" :"+i);
		}
	}
	static void show2(ArrayDeque<Long> dt) {		//上手くいかなかった時用
		long element=0;
		while(dt.size()>0) {
			element=dt.removeFirst();
			System.out.print(element);
		}
		System.out.println("\n");
	}
	static void show2(List<Object> dt) {		//上手くいかなかった時用
	 	for(int i=0; i<dt.size(); i++) {
			System.out.print(dt.get(i)+",");
		}
		System.out.println("\n");
	}

	private static void prtlnas(int[] array) {
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<array.length; i++) {
			out.println(array[i]);
		}
		out.flush();
	}
	private static void prtlnas(long[] array) {
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<array.length; i++) {
			out.println(array[i]);
		}
		out.flush();
	}
	private static void prtlnas(ArrayList<Object> array) {
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<array.size(); i++) {
			out.println(array.get(i));
		}
		out.flush();
	}
	private static void prtspas(int[] array) {
		PrintWriter out = new PrintWriter(System.out);
		out.print(array[0]);
		for(int i=1; i<array.length; i++) {
			out.print(" "+array[i]);
		}
		out.println();
		out.flush();
	}
	private static void prtspas(long[] array) {
		PrintWriter out = new PrintWriter(System.out);
		out.print(array[0]);
		for(int i=1; i<array.length; i++) {
			out.print(" "+array[i]);
		}
		out.println();
		out.flush();
	}
	private static void prtspas(ArrayList<Integer> array) {
		PrintWriter out = new PrintWriter(System.out);
		out.print(array.get(0));
		for(int i=1; i<array.size(); i++) {
			out.print(" "+array.get(i));
		}
		out.println();
		out.flush();
	}


	static class Vector {
		int x,y;
		public Vector(int sx, int sy) {
			this.x=sx;
			this.y=sy;
		}
	}

	static class FastScanner {
		private final InputStream in = System.in;
		private final byte[] buffer = new byte[1024];
		private int ptr = 0;
		private int buflen = 0;
		private boolean hasNextByte() {
			if(ptr < buflen) {
				return true;
			}else{
				ptr = 0;
				try {
					buflen = in.read(buffer);
				} catch (IOException e) {
					e.printStackTrace();
				}
				if(buflen <= 0) {
					return false;
				}
			}
			return true;
		}
		private int readByte() {
			if(hasNextByte()) return buffer[ptr++];
			else return -1;
		}
		private static boolean isPrintableChar(int c) {
			return (33 <= c) && (c <= 126);
		}
		public boolean hasNext() {
			while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
			return hasNextByte();
		}
		public String next() {
			if(!hasNext()) throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while(isPrintableChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		public long nexL() {
			if(!hasNext()) throw new NoSuchElementException();
			long n = 0;
			boolean minus = false;
			int b = readByte();
			if(b == '-') {
				minus = true;
				b = readByte();
			}
			if(b < '0' || '9' < b) {
				throw new NumberFormatException();
			}
			while(true) {
				if('0' <= b && b <= '9') {
					n *= 10;
					n += b - '0';
				}else if(b == -1 || !isPrintableChar(b) || b == ':') {
					return minus ? -n : n;
				}else{
					throw new NumberFormatException();
				}
				b = readByte();
			}
		}
		public int nexI() {
			long nl = nexL();
			if(nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
			return (int) nl;
		}
		public double nexD() { return Double.parseDouble(next());}
		//aはarray
		public void ai(int[]... array) {
			for(int i=0; i<array[0].length; i++) {
				for(int j=0; j<array.length; j++) {
					array[j][i] = nexI();
				}
			}
			return;
		}
		public void al(long[]... array) {
			for(int i=0; i<array[0].length; i++) {
				for(int j=0; j<array.length; j++) {
					array[j][i] = nexL();
				}
			}
			return;
		}
		public void aimin1(int[] array) {
		 	for(int i=0; i<array.length; i++) {
		 		array[i] = nexI()-1;
		 	}
		 	return;
		}
		public void aD(double[] array) {
		 	for(int i=0; i<array.length; i++) {
		 		array[i] = nexD();
		 	}
		 	return;
		}
		public void ai2d(int[][] array) {
			for(int i=0; i<array.length; i++) {
				for(int j=0; j<array[0].length; j++) {
					array[i][j] = nexI();
				}
			}
			return;
		}
	}

}
//END OF THE CODE