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 $$$3_{11} + 4_{11} + 100_{11} + 4_{11} = 110_{11} = 1 ⋅ 11^2 + 1 ⋅ 11 = 132_{10}. It can be shown that it is impossible for Alice to get a larger sum than 132_{10}$$$.
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template <class T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <class K,class V> using omap = tree<K, V, less<K>, rb_tree_tag, tree_order_statistics_node_update>;
void __print(int x){cout<<x;}void __print(long long x){cout<<x;}
void __print(double x){cout<<x;}void __print(long double x){cout<<x;}
void __print(char x){cout<<'\''<<x<<'\'';}void __print(const char *x){cout<<'\"'<<x<<'\"';}
void __print(const string &x){cout<<'\"'<<x<<'\"';}void __print(bool x){cout<<(x?"True":"False");}
template<typename T,typename V>
void __print(const pair<T,V>&x){cout<<'{';__print(x.first);cout<<',';__print(x.second);cout<<'}';}
template<typename T>
void __print(const T &x){int f=0;cout<<'{';for(auto &i:x)cout<<(f++?",":""),__print(i);cout<<"}";}
void _print(){cout<<"]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cout << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cout << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif

#define lp(i,a,b)       for (int i=a;i<=b;i++)
#define rp(i,a,b)       for (int i=a;i>=b;i--)
#define ms(a,x)         memset(a,x,sizeof a)
//#define int             long long 
#define ff              first
#define ss              second
#define all(a)          a.begin(),a.end()
#define rall(a)         a.rbegin(),a.rend()
#define pb              push_back
#define nl              cout<<"\n"
#define index           find_by_order
#define less            order_of_key
#define gcd(a,b)        __gcd((a),(b))
#define lcm(a,b)        (((a)*(b))/(gcd(a,b)))
#define sq(a)           ((a)*(a))
#define sz(a)           (int) a.size()
#define mod             1000000007

void solve()
{
  string s;
  int k;
  cin>>s>>k;
  vector<int>ans;
  int n=sz(s);
  lp(i,0,n-1)
  {
    int x=s[i]-'0';
    if(x)
    {
      int cnt=n-i-1;
      int base=1;
      while(cnt--)
        base*=10;
      while(x--)
        ans.pb(base);
    }
  }
  while(sz(ans)>k)
  {
    int x=ans.back();
    ans.pop_back();
    ans.back()+=x;
  }
  if(sz(ans)==k)
  {
    for(int i:ans)
      cout<<i<<' ';
    nl;
    return;
  }
  int need=k-sz(ans);
  priority_queue<int>q;
  vector<int>now;
  lp(i,0,sz(ans)-1)
  {
    if(ans[i]>1)
      q.push(-ans[i]);
    else
      now.pb(ans[i]);
  }
  while(!q.empty())
  {
    int x=-q.top();
    q.pop();
    if(need==0 or x==1)
    {
      if(x==1)
        need--;
      now.pb(x);
      continue;
    }
    if(x>10)
    {
      string kos=to_string(x);
      n=sz(kos);
      n-=2;
      int vim=1,dig=kos[0]-'0';
      while(n--)
        vim*=10;
      if(dig>1)
      {
        vim*=10;
        debug(dig,vim);
        if(need>dig)
        {
          lp(i,1,dig)
            q.push(-vim);
          need-=dig-1;
        }
        else
        {
          lp(i,1,need)
            q.push(-vim);
          x-=vim;
          if(x)
          q.push(-x);
          need=0;
        }
      }
      else
      {
        if(need>9)
        {
          int cnt=9;
          while(cnt--)
            q.push(-vim);
          need-=9;
        }
        else
        {
          x-=(need*vim);
          while(need--)
            q.push(-vim);
          q.push(-x);
          need=0;
        }
      }
      continue;
    }
    if(x>need)
    {
      int one=need;
      now.pb(x-one);
      while(one--)
        now.pb(1);
      need=0;
    }
    else
    {
      int one=x;
      while(one--)
        now.pb(1);
      need-=x-1;
    }
  }
  for(int i:now)
    cout<<i<<' ';
  nl;
}

signed main()
{
  ios_base::sync_with_stdio(false); 
  cin.tie(NULL); cout.tie(NULL);
  int T=1; 
  cin>>T;
  while(T--) solve();
  return 0;
}
