The nation of Panel holds an annual show called The Number Games, where each district in the nation will be represented by one contestant.

The nation has n districts numbered from 1 to n, each district has exactly one path connecting it to every other district. The number of fans of a contestant from district i is equal to 2^i.

This year, the president decided to reduce the costs. He wants to remove k contestants from the games. However, the districts of the removed contestants will be furious and will not allow anyone to cross through their districts. 

The president wants to ensure that all remaining contestants are from districts that can be reached from one another. He also wishes to maximize the total number of fans of the participating contestants.

Which contestants should the president remove?

Input

The first line of input contains two integers n and k (1 ≤ k < n ≤ 10^6) — the number of districts in Panel, and the number of contestants the president wishes to remove, respectively.

The next n-1 lines each contains two integers a and b (1 ≤ a, b ≤ n, a ≠ b), that describe a road that connects two different districts a and b in the nation. It is guaranteed that there is exactly one path between every two districts.

Output

Print k space-separated integers: the numbers of the districts of which the contestants should be removed, in increasing order of district number.

Examples

Input

6 3
2 1
2 6
4 2
5 6
2 3


Output

1 3 4


Input

8 4
2 6
2 7
7 8
1 2
3 1
2 4
7 5


Output

1 3 4 5

Note

In the first sample, the maximum possible total number of fans is 2^2 + 2^5 + 2^6 = 100. We can achieve it by removing the contestants of the districts 1, 3, and 4.

/**
 * Date: 8 May, 2018
 * Link:
 *
 * @author Prasad-Chaudhari
 * @email prasadc8897@gmail.com
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Stack;

public class The_Number_Games_980_E {

    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        FastIO in = new FastIO();
        int n = in.ni();
        int k = in.ni();
        int i, j;
        int pow[] = new int[20];
        for (i = 0; i < 20; i++) {
            pow[i] = (int) Math.pow(2, i);
        }
        int adja[][] = in.gg(n, n - 1);
        Stack<Integer> st = new Stack<>();
        int parent[] = new int[n + 1];
        byte visited[] = new byte[n + 1];
        int sptable[][] = new int[n + 1][22];
        st.push(n);
        visited[n] = 1;
        for (i = 0; i < n + 1; i++) {
            parent[i] = -1;
        }
        for (int[] arr : sptable) {
            for (j = 0; j < 22; j++) {
                arr[j] = -1;
            }
        }
        while (!st.isEmpty()) {
            int root = st.pop();
            for (int sib : adja[root]) {
                if (visited[sib] == 0) {
                    parent[sib] = root;
                    st.push(sib);
                    visited[sib] = 1;
                }
            }
            sptable[root][0] = parent[root];
            j = 0;
            while (sptable[root][j] != -1) {
                sptable[root][j + 1] = sptable[sptable[root][j]][j];
                j++;
            }
        }
        for (i = 0; i < n; i++) {
            visited[i] = 0;
        }
        visited[n] = 1;
        k = n - k;
        k--;
        int node, depth, curr, curr2;
        for (i = n - 1; k != 0 && i > 0; i--) {
            if (visited[i] == 1) {
                continue;
            }
            depth = 0;
            curr = i;
            while (curr != -1 && visited[curr] == 0) {
                for (j = 0; j < 22; j++) {
                    node = sptable[curr][j];
                    if (node != -1) {
                        if (visited[node] == 1) {
                            break;
                        }
                    } else {
                        break;
                    }
                }
                if (j == 0) {
                    depth++;
                    break;
                }
                depth += pow[j - 1];
                curr = sptable[curr][j - 1];
            }
            if (k != 0 && depth <= k) {
                curr2 = i;
                while (visited[curr2] == 0) {
                    visited[curr2] = 1;
                    curr2 = parent[curr2];
                }
                k -= depth;
            }
        }
        StringBuilder sb = new StringBuilder();
        for (i = 1; i <= n; i++) {
            if (visited[i] == 0) {
                sb.append(i);
                sb.append('\n');
            }
        }
        System.out.println(sb.toString());
    }

    static class FastIO {

        private final BufferedReader br;
        private String s[];
        private int index;

        public FastIO() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
            s = br.readLine().split(" ");
            index = 0;
        }

        public int ni() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public double nd() throws IOException {
            return Double.parseDouble(nextToken());
        }

        public long nl() throws IOException {
            return Long.parseLong(nextToken());
        }

        public String next() throws IOException {
            return nextToken();
        }

        public String nli() throws IOException {
            try {
                return br.readLine();
            } catch (IOException ex) {

            }
            return null;
        }

        public int[] gia(int n) throws IOException {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[] gia(int n, int start, int end) throws IOException {
            validate(n, start, end);
            int a[] = new int[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public double[] gda(int n) throws IOException {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }

        public double[] gda(int n, int start, int end) throws IOException {
            validate(n, start, end);
            double a[] = new double[n];
            for (int i = start; i < end; i++) {
                a[i] = nd();
            }
            return a;
        }

        public long[] gla(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public long[] gla(int n, int start, int end) throws IOException {
            validate(n, start, end);
            long a[] = new long[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[][] gg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        private String nextToken() throws IndexOutOfBoundsException, IOException {
            if (index == s.length) {
                s = br.readLine().split(" ");
                index = 0;
            }
            return s[index++];
        }

        private void validate(int n, int start, int end) {
            if (start < 0 || end >= n) {
                throw new IllegalArgumentException();
            }
        }
    }
}
