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/rope>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

using namespace std;
using namespace __gnu_cxx;

template<class T>
using V = vector<T>;
template<class T>
using VV = V<V<T>>;

using ld = long double;
#define ll long long
using ull = unsigned ll;
using PLL = pair<ll, ll>;
using VLL = V<ll>;
using VB = V<bool>;
using VVB = VV<bool>;
using VVLL = VV<ll>;
using Gr = VVLL;
using MLL = map<ll, ll>;
#define UMLL unordered_map<ll, ll, custom_hash>

#define fast ios_base::sync_with_stdio(0); cin.tie(nullptr); cout.tie(nullptr); cerr.tie(nullptr);

#define R &
#define CR const R

#define FORI(i, a, b) for(ll i = a, max##i = b; i < max##i; ++i)
#define FOR(i, n) FORI(i, 0, n)
#define RFORI(i, a, b) for(ll i = a, min##i = b; i >= min##i; --i)
#define RFOR(i, n) RFORI(i, n, 0)
#define FORA(i, a) for(auto i : a)
#define FORAR(i, a) for(auto R i : a)
#define FORACR(i, a) for(auto CR i : a)
#define ALL(obj) begin(obj), end(obj)
#define Count(q) while(q--)
#define OK cerr << "OK" << endl;

#define mp make_pair
#define pb push_back

//#define DEBUG

template<class T>
T sqr(T x)
{
    return x * x;
}

template<class T>
void cmin(T& a, T const& b)
{
    a = min(a, b);
}

template<class T>
void cmax(T& a, T const& b)
{
    a = max(a, b);
}

void YES(bool g, ostream R os, bool upper = true)
{
    if(g)
        if(upper)
            os << "YES";
        else
            os << "Yes";
    else
        if(upper)
            os << "NO";
        else
            os << "No";

    os << "\n";
}

template<class T>
void show(T CR t, ostream R os = cerr)
{
    FORACR(i, t)
        os << i << " ";
    os << "\n";
}

template<class T>
void show2d(T CR t, ostream R os = cerr)
{
    FORACR(i, t)
        show(i, os);
    os << "\n";
}

constexpr ll MOD = 998244353; //1e9 + 7;
constexpr ll len = 1e4 + 10;

constexpr ll INF = 1e15, MINF = -INF;

constexpr ld PI = atanl(1.0L) * 4;
constexpr ld eps = 1e-9, EPS = 1e-9;

struct custom_hash
{
    static uint64_t splitmix64(uint64_t x)
    {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator() (uint64_t x) const
    {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

//arr
constexpr ll N = 30;
array<ll, N> r;
void init()
{
    FOR(s, N)
        for(ll i = 0; i <= min(s, 9LL); ++i)
            r[s] += s - i <= 9;
}

bool sol(string s, ll n, V<string> R res)
{
    if(n <= 0)
        return true;

    ll cnt = 0;
    FOR(i, s.size())
    {
        cnt = 10 * cnt + s[i] - '0';
        //cerr << s << " " << i << " -> " << cnt << "\n";

        string t = s.substr(i + 1);
        //cerr << t << "\n";

        if(n - cnt <= 0 || sol(t, n - cnt, res))
        {
            string f(s.size() - i, '0');
            f[0] = '1';

            while(res.size() + 1 < n)
            {
                --cnt;
                res.pb(f);
            }

            if(n - cnt <= 0)
                f = '0' + t;

            f[0] = cnt + '0';
            res.pb(f);

            return true;
        }

        res.clear();
    }

    return false;
}

void solve(istream R is, ostream R os)
{
    string s;
    is >> s;
    ll n;
    is >> n;

    V<string> res;
    assert(sol(s, n, res));

    show(res, os);
}

void tester(istream R is, ostream R os)
{
    auto seed = time(nullptr);
    //cerr << "seed: " << seed << "\n";
    srand(seed);
    fast
    init();
    ll q = 1;
    is >> q;

    os << setprecision(999);
    Count(q)
        solve(is, os);
}

int main()
{
    //ifstream in("text.in");
    //ofstream out("text.out");

    tester(cin, cout);
}
