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.BufferedReader;
    import java.io.FileInputStream;
    import java.io.FileNotFoundException;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.util.*;
    import java.io.PrintStream;
                //import java.util.*;

            public class Solution {

                public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;

                static class FastScanner {

                        BufferedReader br;
                        StringTokenizer st ;

                        FastScanner(){
                            br =  new BufferedReader(new InputStreamReader(System.in));
                            st = new StringTokenizer("");
                        }

                        FastScanner(String file) {

                            try {
                                br =  new BufferedReader(new InputStreamReader(new FileInputStream(file)));
                                st = new StringTokenizer("");
                            } catch (FileNotFoundException e) {
                                // TODO Auto-generated catch block
                                System.out.println("file not found");
                                e.printStackTrace();
                            }
                            
                        }
                        

                        String next() {
                            while (!st.hasMoreTokens())
                                try {
                                    st = new StringTokenizer(br.readLine());
                                } catch (IOException e) {
                                }
                            return st.nextToken();
                        }

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

                        long nextLong() {
                            return Long.parseLong(next());
                        }
                        String readLine() throws IOException{
                            return br.readLine();
                        }
                    }
                                        
                static class Pair<T,X>{
                    T first;
                    X second;
                    Pair(T first,X second){
                        this.first = first;
                        this.second = second;
                    }

                    @Override
                    public int hashCode(){
                        return Objects.hash(first,second);
                    }

                    @Override
                    public boolean equals(Object obj){
                        return obj.hashCode() == this.hashCode();
                    }

                }

            
            public static void main(String[] args) throws Exception {
                
                FastScanner s = new FastScanner();

                PrintStream debug = null;
                
                if(LOCAL){
                    s = new FastScanner("src/input.txt");
                    PrintStream o = new PrintStream("src/sampleout.txt");
                    debug = new PrintStream("src/debug.txt");
                    System.setOut(o);
                }

                int pxor[] = new int[(3*100000) + 1];

                for(int i=1;i<(3*100000) + 1;i++){
                    pxor[i] = i ^ pxor[i-1];
                }

                int tcr = s.nextInt();

                
                for(int tc=0;tc<tcr;tc++){
                    
                    int a = s.nextInt();
                    int b = s.nextInt();

                    StringBuilder sb = new StringBuilder();


                    List<Long> list = solve(a,b);

                    for(Long num : list){
                        sb.append(num);
                        sb.append(" ");
                    }

                    println(sb.toString());
                    
                }
                
            }

            public static List<Long> solve(long num,int req){

                List<Long> ans = new ArrayList<>();

                if(req == 0){
                    return ans;
                }

                if(req == 1){
                    ans.add(num);
                    return ans;
                }

                if(num == req){
                    for(long i=0;i<num;i++){
                        ans.add(1l);
                        return ans;
                    }
                }

                int l = len(num);

                int st = l - 1;

                boolean poss = false;

                while(st > 0){

                    long digit = num / (long)(Math.pow(10,st));

                    boolean done = false;

                    for(long crd = digit;crd>0;crd--){
                        if(num - (long)(crd * Math.pow(10,st)) >= req){
                            List<Long> temp = solve(num - (long)(crd * Math.pow(10,st)),req - 1);
                            ans.add(crd * (long)Math.pow(10,st));
                            ans.addAll(temp);
                            return ans;
                        }
                    }

                    st--;
                }

                for(int i=0;i<req - 1;i++){ans.add(1l);}
                ans.add(num - (req - 1));
                return ans;

            }



            static int len(long num){
                return Long.toString(num).length();
            }

            static long mulmod(long a, long b,long mod)
            {
                return ((a%mod) * (b%mod)) % mod;
            }


            public static void dbg(PrintStream ps,Object... o) throws Exception{
                if(ps == null){
                    return;
                }
                Debug.dbg(ps,o);
            }

        
    

            public static long modpow(long num,long pow,long mod){

                long val = num;
                long ans = 1l;

                while(pow > 0l){
                    
                    long bit = pow & 1l;

                    if(bit == 1){
                        ans = (ans * (val%mod))%mod;
                    }

                    val = (val * val) % mod;
                    pow = pow >> 1;
                }

                return ans;

            }

            public static char get(int n){
                return (char)('a' + n);
            }

            public static long[] sort(long arr[]){
                List<Long> list = new ArrayList<>();
                for(long n : arr){list.add(n);}
                Collections.sort(list);
                for(int i=0;i<arr.length;i++){
                    arr[i] = list.get(i);
                }
                return arr;
            }

            public static int[] sort(int arr[]){
                List<Integer> list = new ArrayList<>();
                for(int n : arr){list.add(n);}
                Collections.sort(list);
                for(int i=0;i<arr.length;i++){
                    arr[i] = list.get(i);
                }
                return arr;
            }

            // return the (index + 1)
            // where index is the pos of just smaller element
            // i.e count of elemets strictly less than num
            public static int justSmaller(long arr[],long num){
                //  System.out.println(num+"@");
                int st = 0;
                int e = arr.length - 1;
        
                int ans = -1;
        
                while(st <= e){
        
                    int mid = (st + e)/2;
        
                    if(arr[mid] >= num){
                        e = mid - 1;
                    }else{
                        ans = mid;
                        st = mid + 1;
                    }
        
                }
        
        
                return ans + 1;
        
            }
            
            //return (index of just greater element)
            //count of elements smaller than or equal to num

            public static int justGreater(long arr[],long num){
                int st = 0;
                int e = arr.length - 1;
        
                int ans = arr.length;
        
                while(st <= e){
                    
                    int mid = (st + e)/2;
        
                    if(arr[mid] <= num){
                        st = mid + 1;
                    }else{
                        ans = mid;
                        e = mid - 1;
                    }
                }
        
                return ans;
        
            }
        
            

            public static void println(Object obj){
                System.out.println(obj.toString());
            }

            public static void print(Object obj){
                System.out.print(obj.toString());
            }

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

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

                return gcd(b,a%b);
            }

            public static int find(int parent[],int v){
                if(parent[v] == v){
                    return v;
                }
                
                return parent[v] = find(parent, parent[v]);
            }

        

            public static List<Integer> sieve(){
            
                    List<Integer> prime = new ArrayList<>();

                    int arr[] = new int[100001];

                Arrays.fill(arr,1);

                arr[1] = 0;
                arr[2] = 1;

                for(int i=2;i<=100000;i++){
                    
                    if(arr[i] == 1){
                        
                        prime.add(i);

                        for(long j = (i*1l*i);j<100001;j+=i){
                            arr[(int)j] = 0;
                        }
                    }
                }

                return prime;
            }

            static boolean isPower(long n,long a){
                
                long log = (long)(Math.log(n)/Math.log(a));

                long power = (long)Math.pow(a,log);

                if(power == n){return true;}

                return false;
            }


            private static int mergeAndCount(int[] arr, int l,int m, int r)
            {

                // Left subarray
                int[] left =  Arrays.copyOfRange(arr, l, m + 1);

                // Right subarray
                int[] right = Arrays.copyOfRange(arr, m + 1, r + 1);

                int i = 0, j = 0, k = l, swaps = 0;

                while (i < left.length && j < right.length) {
                    if (left[i] <= right[j])
                        arr[k++] = left[i++];
                    else {
                        arr[k++] = right[j++];
                        swaps += (m + 1) - (l + i);
                    }
                }
                while (i < left.length)
                    arr[k++] = left[i++];
                while (j < right.length)
                    arr[k++] = right[j++];
                return swaps;
            }

            // Merge sort function
            private static int mergeSortAndCount(int[] arr, int l,int r)
            {

                // Keeps track of the inversion count at a
                // particular node of the recursion tree
                int count = 0;

                if (l < r) {
                    int m = (l + r) / 2;

                    // Total inversion count = left subarray count
                    // + right subarray count + merge count

                    // Left subarray count
                    count += mergeSortAndCount(arr, l, m);

                    // Right subarray count
                    count += mergeSortAndCount(arr, m + 1, r);

                    // Merge count
                    count += mergeAndCount(arr, l, m, r);
                }

                return count;
            }

            static class Debug{
                //change to System.getProperty("ONLINE_JUDGE")==null; for CodeForces
                public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;

                

                private static <T> String ts(T t) {
                    if(t==null) {
                        return "null";
                    }
                    try {
                        return ts((Iterable) t);
                    }catch(ClassCastException e) {
                        if(t instanceof int[]) {
                            String s = Arrays.toString((int[]) t);
                            return "{"+s.substring(1, s.length()-1)+"}\n";
                        }else if(t instanceof long[]) {
                            String s = Arrays.toString((long[]) t);
                            return "{"+s.substring(1, s.length()-1)+"}\n";
                        }else if(t instanceof char[]) {
                            String s = Arrays.toString((char[]) t);
                            return "{"+s.substring(1, s.length()-1)+"}\n";
                        }else if(t instanceof double[]) {
                            String s = Arrays.toString((double[]) t);
                            return "{"+s.substring(1, s.length()-1)+"}\n";
                        }else if(t instanceof boolean[]) {
                            String s = Arrays.toString((boolean[]) t);
                            return "{"+s.substring(1, s.length()-1)+"}\n";
                        }
                        try {
                            return ts((Object[]) t);
                        }catch(ClassCastException e1) {
                            return t.toString();
                        }
                    }
                }
                private static <T> String ts(T[] arr) {
                    StringBuilder ret = new StringBuilder();
                    ret.append("{");
                    boolean first = true;
                    for(T t: arr) {
                        if(!first) {
                            ret.append(", ");
                        }
                        first = false;
                        ret.append(ts(t));
                    }
                    ret.append("}");
                    return ret.toString();
                }
                private static <T> String ts(Iterable<T> iter) {
                    StringBuilder ret = new StringBuilder();
                    ret.append("{");
                    boolean first = true;
                    for(T t: iter) {
                        if(!first) {
                            ret.append(", ");
                        }
                        first = false;
                        ret.append(ts(t));
                    }
                    ret.append("}");
                    return ret.toString();
                }
                public static void dbg(PrintStream ps,Object... o) throws Exception {
                    if(LOCAL) {
                        System.setErr(ps);
                        System.err.print("Line #"+Thread.currentThread().getStackTrace()[2].getLineNumber()+": [");
                        for(int i = 0; i<o.length; i++) {
                            if(i!=0) {
                                System.err.print(", ");
                            }
                            System.err.print(ts(o[i]));
                        }
                        System.err.println("]");
                    }
                }
            }

    }