#include <iostream>
#include <fstream>
#include <vector>
#include <algorithm>
#include <queue>

using namespace std;

#define nmax 10005

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

vector<int> gf[nmax], cpy[nmax];
int n, k, viz[nmax], d[nmax];
int rez[nmax];
bool special[nmax];
int st[nmax], _sz;
queue<pair<int, int> > q;
int t[nmax];
int sol[nmax];

typedef vector<int>::iterator it_vec;
void citeste(){

    f >> n;
    f >> k;
    for(int i=1; i<n; i++){
        int x, y;
        f >> x >>  y;
        gf[x].push_back(y);
        gf[y].push_back(x);
    }

}

int check(int val){

    int cnt = 0;
    rez[0] = 0;
    for(int i=1; i<=n; i++) cpy[i] = gf[i], viz[i]=0, d[i]=0, t[i] = 0;
    for(;q.size(); q.pop());

    for(int i=1; i<=n; i++){
        if (cpy[i].size()==1){
            q.push(make_pair(i,val));
        }
    }

    for(; q.size(); ){
        int nod = (q.front()).first;
        int x = (q.front()).second;
        d[nod] = x;
        q.pop();
        int vc = cpy[nod][0];
        cpy[nod].clear();

        for(it_vec j=cpy[vc].begin(); j!=cpy[vc].end(); j++){
            if (*j == nod){
                cpy[vc].erase(j);
                break;
            }
        }
        if (viz[vc] == 0 && x-1 == 0){
            viz[vc] = 1;
            rez[++rez[0]] = vc;
        }
        if ( t[vc]<=n/2 )++t[vc],  q.push(make_pair(vc,x-1));
    }
    for(int i=1; i<=n; i++){

        if (d[i] < 0)
        if (d[i] < (-1)*(val)){
            return 0;
        }
    }
    if (cnt > k) return 0;
    if (rez[0]< k)
        for(int i=1; i<=n; i++){
            if (viz[i] == 0) rez[++rez[0]] = i;
            if (rez[0] == k) break;
        }
    return 1;

}

void rezolva(){

    int st=0;
    int dr = n+1;
    while(dr-st>1){
        int mij =(st+dr) / 2;
        if (check(mij)){
            sol[0] = 0;
            for(int i=1; i<=rez[0]; i++) sol[++sol[0]] = rez[i];
            dr = mij;
        }else st = mij;
    }

    g << dr << "\n";
    sort(sol+1, sol+sol[0]+1 );
    for(int i=1; i<=sol[0]; i++) g << sol[i] << " ";

}

int main(){

    citeste();
    rezolva();

}