#include <bits/stdc++.h>
#define Nmax 1005
using namespace std;

ifstream f("salvare.in");
ofstream g("salvare.out");

int n,k;
list <int> G[Nmax];
queue < pair<int,int> > q;
int nr_ans;
bitset <Nmax> solution;
bitset <Nmax> s;
bitset <Nmax> viz;

void set_bitset()
{
    nr_ans=0;
    for(int i=1;i<=n;i++)
    {
        solution[i]=s[i];
        if(s[i]) ++nr_ans;
    }
}

bool sol_valid(int dist)
{
    int i,nr_saves=0;
    while(!q.empty())
        q.pop();
    viz.reset();
    s.reset();
    for(i=1;i<=n;i++)
         if((int)G[i].size()==1)
        {
            q.push({i,dist});
            viz[i]=true;
        }
    int x,y;
    while(!q.empty())
    {
        x=q.front().first;
        y=q.front().second;
        q.pop();
        viz[x]=true;
        if(!y)
        {
            ++nr_saves;
            s[x]=true;
            y=dist;
        }
        if(nr_saves>k) return false;
        for(const auto &it:G[x])
            if(!viz[it])
            {
                viz[it]=true;
                q.push({it,y-1});
            }
    }
    return nr_saves<=k;
}

int main()
{
    int x,y,i;
    f>>n>>k;
    for(i=1;i<n;i++)
    {
        f>>x>>y;
        G[x].push_back(y);
        G[y].push_back(x);
    }
    int lo=1,hi=n-1,mid,ans=n-1;
    while(lo<=hi)
    {
        mid=(lo+hi)>>1;
        if(sol_valid(mid))
        {
            ans=mid;
            set_bitset();
            hi=mid-1;
        }
        else lo=mid+1;
    }
    g<<ans<<'\n';
    if(nr_ans<k)
    {
        i=1;
        while(nr_ans<k)
        {
            while(solution[i]) i++;
            solution[i]=true;
            nr_ans++;
        }
    }
    for(i=1;i<=n;i++)
        if(solution[i]) g<<i<<' ';

    return 0;
}