On the board, Bob wrote n positive integers in [base](https://en.wikipedia.org/wiki/Positional_notation#Base_of_the_numeral_system) 10 with sum s (i. e. in decimal numeral system). Alice sees the board, but accidentally interprets the numbers on the board as base-11 integers and adds them up (in base 11).

What numbers should Bob write on the board, so Alice's sum is as large as possible?

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases. The description of the test cases follows.

The only line of each test case contains two integers s and n (1 ≤ s ≤ 10^9; 1 ≤ n ≤ min(100, s)) — the sum and amount of numbers on the board, respectively. Numbers s and n are given in decimal notation (base 10).

Output

For each test case, output n positive integers — the numbers Bob should write on the board, so Alice's sum is as large as possible. If there are multiple answers, print any of them.

Example

Input


6
97 2
17 1
111 4
100 2
10 9
999999 3


Output


70 27 
17 
3 4 100 4
10 90
1 1 2 1 1 1 1 1 1 
999900 90 9

Note

In the first test case, 70_{10} + 27_{10} = 97_{10}, and Alice's sum is $$$70_{11} + 27_{11} = 97_{11} = 9 ⋅ 11 + 7 = 106_{10}. (Here x_b represents the number x in base b.) It can be shown that it is impossible for Alice to get a larger sum than 106_{10}$$$.

In the second test case, Bob can only write a single number on the board, so he must write 17.

In the third test case, 3_{10} + 4_{10} + 100_{10} + 4_{10} = 111_{10}, and Alice's sum is $$$3_{11} + 4_{11} + 100_{11} + 4_{11} = 110_{11} = 1 ⋅ 11^2 + 1 ⋅ 11 = 132_{10}. It can be shown that it is impossible for Alice to get a larger sum than 132_{10}$$$.
import java.util.*;
import java.io.*;

public class D_1567 {
	
	static ArrayList<Integer>[] list;
	public static void add(int s) {
		long mul = 10;
		for(int i = 0; i < 10; i++) {
			if(s / mul == 0) {
				list[i].add(s);
				break;
			}
			mul *= 10;
		}
	}
	
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int t = sc.nextInt();
		while(t-->0) {
			int s = sc.nextInt(), n = sc.nextInt();
			list = new ArrayList[10];
			for(int i = 0; i < 10; i++)
				list[i] = new ArrayList<>();
			
			long mod = 10;
			n--;
			while(true) {
				if(n == 0)
					break;
				if(s % mod == 0) {
					mod *= 10;
				} else {
					long x = s % mod;
					long y = mod / 10;
					//System.out.println(n + " " + x + " " + y + " " + s);
					if(x == s && s / y == 1)
						break;
					add((int)y);
					s -= y;
					n--;
				}
			}
			add(s);
			//System.out.println(Arrays.deepToString(list));
			//System.out.println(n);
			while(n-->0) {
				int mul = 1;
				boolean flag = false;
				big:
				for(int i = 0; i < 10; i++) {
					for(int j = 0; j < list[i].size(); j++)
						if(list[i].get(j) / mul > 1) {
							int x = list[i].get(j);
							x -= mul;
							list[i].add(mul);
							list[i].set(j, x);
							flag = true;
							break big;
						}
					mul *= 10;
				}
				
				if(!flag) {
					mul = 1;
					for(int i = 1; i < 10; i++) {
						if(list[i].size() > 0) {
							int x = list[i].get(0);
							list[i].remove(0);
							list[i - 1].add(x - mul);
							list[i - 1].add(mul);
							break;
						}
						mul *= 10;
					}
				}
			}
			
			//System.out.println(Arrays.deepToString(list));
			
			for(int i = 0; i < 10; i++)
				for(int j : list[i])
					pw.print(j + " ");
			pw.print("\n");
		}
		
		pw.flush();
	}

	public static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

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

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

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

		public int[] nextIntArray(int n) throws IOException {
			int[] array = new int[n];
			for (int i = 0; i < n; i++)
				array[i] = nextInt();
			return array;
		}

		public Integer[] nextIntegerArray(int n) throws IOException {
			Integer[] array = new Integer[n];
			for (int i = 0; i < n; i++)
				array[i] = new Integer(nextInt());
			return array;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] array = new long[n];
			for (int i = 0; i < n; i++)
				array[i] = nextLong();
			return array;
		}

		public double[] nextDoubleArray(int n) throws IOException {
			double[] array = new double[n];
			for (int i = 0; i < n; i++)
				array[i] = nextDouble();
			return array;
		}

		public static int[] shuffle(int[] a) {
			int n = a.length;
			Random rand = new Random();
			for (int i = 0; i < n; i++) {
				int tmpIdx = rand.nextInt(n);
				int tmp = a[i];
				a[i] = a[tmpIdx];
				a[tmpIdx] = tmp;
			}
			return a;
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}
