#include <bits/stdc++.h>

using namespace std;

const int NMAX = 1010;

int N, K;
int nodes[NMAX];
vector<int> G[NMAX];

int DFS(int node, int from, int curr, int max) {
    int ret = 0;

    if (curr == 1)
        nodes[node] = ret = 1;

    for (int next : G[node]) {
        if (next == from)
            continue;
            ret += DFS(next, node, curr % (max + 1) + 1, max);
    }

    return ret;
}

int main() {
	ios_base::sync_with_stdio(false);
	#ifndef ONLINE_JUDGE
	assert(freopen("salvare.in", "r", stdin) != NULL);
    assert(freopen("salvare.out", "w", stdout) != NULL);
    assert(freopen("debug.err", "w", stderr) != NULL);
    #endif

    int i, j, x, y;

    cin >> N >> K;
    for (i = 0; i < N - 1; ++i) {
        cin >> x >> y;
        G[x].push_back(y);
        G[y].push_back(x);
    }

    int left = 0, right = N, mid = (left + right), sol = -1;
    while (left <= right) {
        bool ok = 0;
        for (int root = 1; root <= N; ++root)
            if (DFS(root, -1, 1, mid) <= K) {
                ok = 1;
                break;
            }

        if (ok) {
            sol = mid;
            right = mid - 1;
        } else
            left = mid + 1;

        mid = (left + right) / 2;
    }

    cout << sol << '\n';
    for (int root = 1; root <= N; ++root) {
        memset(nodes, 0, sizeof(nodes));
        int num = K - DFS(root, -1, 1, sol);

        if (num < 0)
            continue;

        for (i = 1; i <= N; ++i)
            if (nodes[i] == 1)
                cout << i << ' ';
            else if (num) {
                --num;
                cout << i << ' ';
            }
        cout << '\n';

        break;
    }

	return 0;
}