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.math.*;
import java.io.*;

public class CF980E {

	class Entry {
		int u, h, chainNo;
		public Entry(int uu, int hh, int cc) {
			u = uu;
			h = hh;
			chainNo = cc;
		}
	}

	class Graph {
		int n, globalChainNo, globalNodeNo, root, numTaken;
		int[] idx;
		int[][] adj;
		int[] p, nodeIdx, pos, head, chain, depth, subSize;
		boolean[] taken;
		BIT bit;
		public Graph(int nn, int[] count) {
			adj = new int[n = nn][];
			for(int i = 0 ; i < n ; i++) adj[i] = new int[count[i]];
			idx = new int[n];
			root = n - 1;
			taken = new boolean[n];
			taken[root] = true;
			numTaken = 1;
		}
		void add(int u, int v) {
			adj[u][idx[u]++] = v;
			adj[v][idx[v]++] = u;
		}
		int dist(int u, int v) { return depth[u] + depth[v] - (2 * depth[lca(u, v)]); }
		void constructHLD() {
			p = new int[n];
			pos = new int[n];
			head = new int[n];
			chain = new int[n];
			depth = new int[n];
			nodeIdx = new int[n];
			subSize = new int[n];
			globalNodeNo = 1;
			globalChainNo = 0;
			Arrays.fill(subSize, 1);
			Arrays.fill(head, -1);
			p[root] = -1;
			dfs();
			HLD();
			bit = new BIT(globalNodeNo);
		}
		void dfs() {
			Deque<Integer> q1 = new ArrayDeque<>();
			Stack<Integer> q2 = new Stack<>();
			q1.add(root);
			q2.add(root);
			while(!q1.isEmpty()) {
				int u = q1.pop();
				for(int v : adj[u]) {
					if(p[u] != v) {
						depth[v] = depth[u] + 1;
						p[v] = u;
						q1.add(v);
						q2.add(v);
					}
				}
			}
			while(!q2.isEmpty()) {
				int u = q2.pop();
				for(int v : adj[u])
					if(p[u] != v)
						subSize[u] += subSize[v];
			}
		}
		void HLD() {
			Deque<Entry> q = new ArrayDeque<>();
			q.add(new Entry(root, root, globalChainNo++));
			while(!q.isEmpty()) {
				Entry e = q.poll();
				int u = e.u, h = e.h, chainNo = e.chainNo;
				head[u] = h;
				chain[u] = chainNo;
				if(u != h) nodeIdx[u] = nodeIdx[p[u]] + 1;
				else nodeIdx[u] = globalNodeNo++;
				globalNodeNo = Math.max(globalNodeNo, nodeIdx[u] + 1);
				int heavyNode = -1, max = 0;
				for(int v : adj[u]) {
					if(p[u] != v && subSize[v] > max) {
						max = subSize[v];
						heavyNode = v;
					}
				}
				if(heavyNode != -1) {
					pos[heavyNode] = pos[u] + 1;
					q.addFirst(new Entry(heavyNode, h, chainNo));
				}
				for(int v : adj[u]) {
					if(v != p[u] && v != heavyNode) {
						pos[v] = 0;
						q.addLast(new Entry(v, v, globalChainNo++));
					}
				}
			}
		}
		int lca(int u, int v) {
			while(chain[u] != chain[v]) {
				if(chain[u] > chain[v]) u = p[head[u]];
				if(chain[v] > chain[u]) v = p[head[v]];
			}
			return pos[u] < pos[v] ? u : v;
		}
		void takeNode(int u) {
			int numNodes = 0;
			int tmpNode = u;
			while(tmpNode != -1) {
				numNodes += bit.rangeSum(nodeIdx[head[tmpNode]], nodeIdx[tmpNode]);
				tmpNode = p[head[tmpNode]];
			}
			if(n - (numTaken + numNodes) >= k) {
				numTaken += numNodes;
				while(!taken[u]) {
					bit.update(nodeIdx[u], -1);
					taken[u] = true;
					u = p[u];
				}
			}
		}
		class BIT {
			int n; long table[];
			public BIT(int nn) {
				table = new long[n = (nn + 10)];
				for(int i = 1 ; i < n ; i++)
					table[i] = i & -i;
				update(nodeIdx[root], -1);
			}
			void update(int i, long delta) {
				while(i < n) {
					table[i] += delta;
					i += i & -i;
				}
			}
			long sum(int i) {
				long sum = 0;
				while(i > 0) {
					sum += table[i];
					i -= i & -i;
				}
				return sum;
			}
			long rangeSum(int i, int j) {
				return sum(j) - sum(i - 1);
			}
		}
	}

	final int MOD = (int) 1e9 + 7;
	final double ERROR = 1e-9;
	final double oo = 1e50;
	int k;

	public CF980E(SuperScanner scan, PrintWriter out) {
		int n = scan.nextInt(); k = scan.nextInt();
		if(k == n) {
			for(int i = 0 ; i < n ; i++)
				out.printf("%d ", i + 1);
			return;
		}
		int[][] adj = new int[2][n];
		int[] count = new int[n];
		for(int i = 0 ; i < n - 1 ; i++) {
			adj[0][i] = scan.nextInt() - 1;
			adj[1][i] = scan.nextInt() - 1;
			count[adj[0][i]]++;
			count[adj[1][i]]++;
		}
		Graph g = new Graph(n, count);
		for(int i = 0 ; i < n - 1 ; i++)
			g.add(adj[0][i], adj[1][i]);
		g.constructHLD();
		for(int i = n - 2 ; i >= 0 ; i--)
			g.takeNode(i);
		for(int i = 0 ; i < n ; i++)
			if(!g.taken[i])
				out.printf("%d ", i + 1);
	}

	static class SuperScanner {
		public int BS = 1 << 16;
		public char NC = (char) 0;
		byte[] buf = new byte[BS];
		int bId = 0, size = 0;
		char c = NC;
		double num = 1;
		BufferedInputStream in;

		public SuperScanner() {
			in = new BufferedInputStream(System.in, BS);
		}

		public SuperScanner(String s) throws FileNotFoundException {
			in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
		}

		public char nextChar() {
			while (bId == size) {
				try {
					size = in.read(buf);
				} catch (Exception e) {
					return NC;
				}
				if (size == -1)
					return NC;
				bId = 0;
			}
			return (char) buf[bId++];
		}

		public int nextInt() {
			return (int) nextLong();
		}

		public long nextLong() {
			num = 1;
			boolean neg = false;
			if (c == NC)
				c = nextChar();
			for (; (c < '0' || c > '9'); c = nextChar()) {
				if (c == '-')
					neg = true;
			}
			long res = 0;
			for (; c >= '0' && c <= '9'; c = nextChar()) {
				res = (res << 3) + (res << 1) + c - '0';
				num *= 10;
			}
			return neg ? -res : res;
		}

		public double nextDouble() {
			double cur = nextLong();
			return c != '.' ? cur : cur + nextLong() / num;
		}

		public String next() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = nextChar();
			while (c > 32) {
				res.append(c);
				c = nextChar();
			}
			return res.toString();
		}

		public String nextLine() {
			StringBuilder res = new StringBuilder();
			while (c <= 32)
				c = nextChar();
			while (c != '\n') {
				res.append(c);
				c = nextChar();
			}
			return res.toString();
		}

		public boolean hasNext() {
			if (c > 32)
				return true;
			while (true) {
				c = nextChar();
				if (c == NC)
					return false;
				else if (c > 32)
					return true;
			}
		}
	}

	public static void main(String[] args) {
		SuperScanner scan = new SuperScanner();
		PrintWriter out = new PrintWriter(System.out);
		new CF980E(scan, out);
		out.close();
	}
}
