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.
import java.util.*;
import java.io.*;
import java.text.*;

public class E980 {

	static int[] p, s, e, dist;
	static ArrayList<Integer>[] adjList;
	static int t = 0;

	public static void getIntervals(int u) {
		Stack<Integer> st = new Stack<Integer>();
		st.add(u << 1 | 1);
		st.add(u << 1);
		while (!st.isEmpty()) {
			int cur = st.pop();
			int ss = cur & 1;
			int idx = cur >> 1;
			if (ss == 0) {
				s[idx] = t++;
				if (p[idx] != -1)
					dist[s[idx]] = dist[s[p[idx]]] + 1;
				for (int x : adjList[idx]) {
					if (s[x] == -1) {
						p[x] = idx;
						st.add(x << 1 | 1);
						st.add(x << 1);
					}
				}
			} else {
				e[idx] = t - 1;
			}
		}
	}

	static class Pair {
		int idx, s;

		public Pair(int idx, int s) {
			this.idx = idx;
			this.s = s;
		}

	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int k = sc.nextInt();
//		int n = (int) 1e6;
//		int k = 19;
		adjList = new ArrayList[n];
		for (int i = 0; i < adjList.length; i++) {
			adjList[i] = new ArrayList<Integer>();
		}

		for (int i = 0; i < n - 1; i++) {
			int u = sc.nextInt() - 1;
			int v = sc.nextInt() - 1;
//			int u = i;
//			int v = i + 1;
			adjList[u].add(v);
			adjList[v].add(u);
		}
		p = new int[n];
		Arrays.fill(p, -1);

//		long start = System.currentTimeMillis();
//		getParent(n - 1);
//		long end = System.currentTimeMillis();
//		System.out.println(end - start);
		s = new int[n];
		e = new int[n];
		dist = new int[n];
		Arrays.fill(s, -1);
//		Arrays.fill(dist, -1);
//		start = System.currentTimeMillis();
		getIntervals(n - 1);
//		end = System.currentTimeMillis();
//		System.out.println(end - start);
//		start = System.currentTimeMillis();
//		getDistance(n - 1);
//		end = System.currentTimeMillis();
//		System.out.println(end - start);
//		pw.println(Arrays.toString(p));
//		pw.println(Arrays.toString(dist));
		int N = 1;
		while (N < n)
			N <<= 1; // padding

//		for (int i = 1; i <= n; i++) {
//			in[i] = dist[i - 1];
//		}
//		start = System.currentTimeMillis();
		SegmentTree sg = new SegmentTree(N);

		int rem = n - k - 1;

		boolean taken[] = new boolean[n];
		taken[n - 1] = true;
		for (int i = n - 2; rem > 0 && i >= 0; i--) {
			if (taken[i])
				continue;
			int q = dist[s[i]] + sg.query(s[i] + 1, s[i] + 1);
			if (q <= rem) {
				rem -= q;
				int cur = i;
				Stack<Integer> path = new Stack<Integer>();
				while (!taken[cur]) {
					taken[cur] = true;
					path.add(cur);
					cur = p[cur];
				}
				while (!path.isEmpty()) {
					cur = path.pop();
					sg.update_range(s[cur] + 1, e[cur] + 1, -1);
				}
			}

		}
//		end = System.currentTimeMillis();
//		System.out.println(end - start);
		for (int i = 0; i < taken.length; i++) {
			if (!taken[i]) {
				pw.print(i + 1 + " ");
			}
		}
		pw.close();
	}

	static class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		int[] sTree, lazy;

		SegmentTree(int N) {
			this.N = N;
			sTree = new int[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new int[N << 1];
		}

		void update_range(int i, int j, int val) // O(log n)
		{
			update_range(1, 1, N, i, j, val);
		}

		void update_range(int node, int b, int e, int i, int j, int val) {
			if (i > e || j < b)
				return;
			if (b >= i && e <= j) {
				lazy[node] += val;
			} else {
				int mid = b + e >> 1;
				
				update_range(node << 1, b, mid, i, j, val);
				update_range(node << 1 | 1, mid + 1, e, i, j, val);

			}

		}

		
		int query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		int query(int node, int b, int e, int i, int j) // O(log n)
		{
//			System.out.println(b+" "+e+" "+node);
			if (i > e || j < b)
				return 0;
			if (b >= i && e <= j)
				return lazy[node];
			int mid = b + e >> 1;

			int q1 = query(node << 1, b, mid, i, j);
			int q2 = query(node << 1 | 1, mid + 1, e, i, j);
			return q1 + q2 + lazy[node];
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader r) {
			br = new BufferedReader(r);
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

	}
}
