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.io.*;
import java.math.*;
import java.util.*;

public class D {

    static final int INF = 0x3f3f3f3f;
    static final long LNF = 0x3f3f3f3f3f3f3f3fL;

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

        initReader();

        int T = nextInt();
        for (int i = 1; i <= T; i++)
            solve();


        pw.flush();
    }

    /*******************************************************************************************************************************/


    public static void solve() throws IOException {
        int s = nextInt();
        int n = nextInt();

        long x = fun(s);
        while (n-- > 0) {
            while (s - x < n) x /= 10;
            if (n == 0) pw.println(s);
            else pw.print(x + " ");
            s -= x;
        }
    }

    public static int fun(int x) {
        if (0 < x && x <= 10) return 1;
        if (10 < x && x <= 100) return 10;
        if (100 < x && x <= 1000) return 100;
        if (1000 < x && x <= 10000) return 1000;
        if (10000 < x && x <= 100000) return 10000;
        if (100000 < x && x <= 1000000) return 100000;
        if (1000000 < x && x <= 10000000) return 1000000;
        if (10000000 < x && x <= 100000000) return 10000000;
        if (100000000 < x && x <= 1000000000) return 100000000;
        throw new Error();
    }


    public static void Solve(BufferedReader reader1, PrintWriter pw1, StringTokenizer tokenizer1) throws IOException {
        reader = reader1;
        pw = pw1;
        tokenizer = tokenizer1;

        int T = nextInt();
        for (int i = 1; i <= T; i++)
            solve();

        pw.flush();
    }

    public static <T> void deBug(T... a) {
        System.out.println(Arrays.toString(a));
    }

    /*******************************************************************************************************************************/


    /*******************************************************************************************************************************/

    static BufferedReader reader;
    static StringTokenizer tokenizer;
    static PrintWriter pw;

    public static void initReader() throws IOException {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

//        reader = new BufferedReader(new FileReader("test.in"));
//        tokenizer = new StringTokenizer("");
//        pw = new PrintWriter(new BufferedWriter(new FileWriter("My answer.out")));
    }

    public static boolean hasNext() {
        try {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(reader.readLine());
            }
        } catch (Exception e) {
            return false;
        }
        return true;
    }

    public static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    public static String nextLine() {
        try {
            return reader.readLine();
        } catch (Exception e) {
            return null;
        }
    }

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

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

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

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