#include <cstdio>
#include <bitset>
#include <vector>
#include <algorithm>
#include <deque>
#define DIMN 1001
using namespace std;
int elem,salv[DIMN],d[DIMN],k,n,root,grad[DIMN];
bitset <DIMN> f;
vector <int> v[DIMN];
deque <int> dq;
void dfs (int nod,int x){
    int i,vecin;
    f[nod]=1;
    if (nod!=root && v[nod].size()==1){ /// frunza
        d[nod]=x;
        return;
    }
    d[nod]=2*x+1;
    for (i=0;i<v[nod].size();i++){
        vecin=v[nod][i];
        if (f[vecin]==0){
            dfs(vecin,x);
            d[nod]=min(d[nod],d[vecin]-1);
        }
    }
    if (d[nod]<=0){ /// nod marcat
        d[nod]=2*x+1;
        salv[++elem]=nod;
    }
}
int verif (int x){
    int i,vecin,nod;
    elem=0;
    for (i=1;i<=n;i++){
        d[i]=2000000000;
        grad[i]=v[i].size();
        if (grad[i]==1){
            d[i]=x;
            dq.push_back(i);
        }
    }
    while (!dq.empty()){
        nod=dq.front();
        //if (x==1)
        //printf ("%d %d\n",nod,d[nod]);
        if (d[nod]==0){
            d[nod]=2*x+1;
            salv[++elem]=nod;
        }
        dq.pop_front();
        if (grad[nod]==0){
            if (d[nod]<=x)
                salv[++elem]=nod;
        }
        for (i=0;i<v[nod].size();i++){
            vecin=v[nod][i];
            grad[vecin]--;
            if (grad[vecin]>=1)
                d[vecin]=min(d[vecin],d[nod]-1);
            if (grad[vecin]==1){
                dq.push_back(vecin);
            }
        }
    }
    if (elem<=k)
        return 1;
    return 0;
}
int main()
{
    FILE *fin=fopen ("salvare.in","r");
    FILE *fout=fopen ("salvare.out","w");
    int i,x,y,st,dr,mid,add,p;
    fscanf (fin,"%d%d",&n,&k);
    for (i=1;i<n;i++){
        fscanf (fin,"%d%d",&x,&y);
        v[x].push_back(y);
        v[y].push_back(x);
    }
    if (k==n){
        fprintf (fout,"0\n");
        for (i=1;i<=n;i++)
            fprintf (fout,"%d ",i);
        return 0;
    }
    st=1;
    dr=n;
    while (st<=dr){
        mid=(st+dr)/2;
        if (verif (mid))
            dr=mid-1;
        else st=mid+1;
    }
    verif (st);
    fprintf (fout,"%d\n",st);
    f.reset();
    for (i=1;i<=elem;i++)
        f[salv[i]]=1;
    add=k-elem;
    p=1;
    while (add){
        if (!f[p]){
            salv[++elem]=p;
            add--;
        }
        p++;
    }
    sort (salv+1,salv+elem+1);
    for (i=1;i<=elem;i++)
        fprintf (fout,"%d ",salv[i]);
    return 0;
}