#include <cstdio>
#include <vector>

using namespace std;

#define NMAX 100100
#define MIN(a,b) (((a)<(b))?(a):(b))
#define MAX(a,b) (((a)>(b))?(a):(b))
#define pb push_back

vector<long long> C[NMAX];
vector<int> A[NMAX];
int N, K, MinK, X[NMAX], F[NMAX], tata[NMAX];
long long BIG, Cmin, lo, hi, md, cost[NMAX], B[NMAX], V[NMAX], U[NMAX], INF;

void dfs(int i)
{
        int j, n = A[i].size();

        F[i] = 1;
        for (j = 0; j < n; j++)
            if (!F[ A[i][j] ])
            {
                tata[ A[i][j] ] = i;
                cost[ A[i][j] ] = C[i][j];
                dfs(A[i][j]);
            }
}

void _try(int i)
{
        int j, n = A[i].size();

        F[i] = 1;
        for (j = 0; j < n; j++)
            if (!F[ A[i][j] ]) _try(A[i][j]);

        for (j = 0; j < n; j++)
        if (tata[i]!=A[i][j])
        {
            V[i] = MAX(V[i], V[ A[i][j] ]+1);
            U[i] = MIN(U[i], U[ A[i][j] ]+1);
        }

        if (md-U[i]>=V[i]) V[i] = -INF;
        else
        if (V[i]+cost[i]<=md);
        else
        {
                U[i] = 0; V[i] = -INF;
                MinK++;
                X[i] = 1;
        }
}

int main()
{
        int i, j, k, nf=0, t;
        long long a = 1000000000, b = 1000000;

        BIG = a*b;

        freopen("salvare.in", "r", stdin);
        freopen("salvare.out", "w", stdout);
        
        scanf("%d%d", &N, &K);
        for (t = 1; t <= N; t++) B[t] = 1;
        for (t = 1; t < N; t++)
        {
                scanf("%d%d", &i, &j); k = 1;
                A[i].pb(j); A[j].pb(i); C[i].pb(k); C[j].pb(k);
        }

        dfs(1);

        INF = ((BIG+1)<<1);
        cost[1] = INF*4;
        md = BIG>>1;
        for (lo = 1, hi = BIG; lo <= hi; md = (lo+hi)>>1)
        {
                for (i = 1; i <= N; i++)
                    V[i] = X[i] = F[i] = 0, U[i] = INF;
                MinK = 0;
                _try(1);
                if (MinK <= K) hi = md-1, Cmin = md;
                else lo = md+1;
        }

        md = Cmin;
        for (i = 1; i <= N; i++) V[i] = X[i] = F[i] = 0, U[i] = INF;
        MinK = 0;
        _try(1);

        for (i = 1; i <= N && MinK < K; i++)
            if (!X[i]) X[i] = 1, MinK++;

        printf("%lld\n", Cmin);
        for (i = 1; i <= N; i++)
            if (X[i]) printf("%d ", i);
        printf("\n");

        return 0;
        
}