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.util.logging.Level;
import java.io.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static final double EPS = 1e-9;
	static long mod = 1000000007;
	static int inf = (int) 1e9 + 2;
	static long[] fac;
	static int[] si;
	static ArrayList<Integer> primes;
	static ArrayList<Integer>[] ad;
	static ArrayList<qu>[] d;
	static edge[] ed;
	static int[] l, ch;
	static int[] occ;
	static long[][] adjMatrix;
	static Queue<Integer>[] can;
	static String s;
	static int[][] memo, P;
	static int n, k;
	static int[] a, pa;
	static boolean[] t;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		n = sc.nextInt();
		k = sc.nextInt();
		
		t = new boolean[n];
		t[n - 1] = true;
		int[] at = new int[n - 1], bt = new int[n - 1], deg = new int[n];
		int [][] adj = new int[n][];
		for (int i = 0; i < n - 1; i++) {
			int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
//			adj[u].add(v);
//			adj[v].add(u);
			at[i] = u;
			bt[i] = v;
			deg[u]++;
			deg[v]++;
		}
		for (int i = 0; i < n; i++)
			adj[i] = new int[deg[i]];
		for (int i = 0; i < n - 1; i++) {
			int u = at[i], v = bt[i];
			adj[u][--deg[u]] = v;
			adj[v][--deg[v]] = u;
 
		}
		int m = 21;
		a = new int[n];
		Queue<Integer> q = new LinkedList();
		q.add(n - 1);
		Arrays.fill(a, -1);
		a[n - 1] = 0;
		pa=new int [n];
		pa[n - 1] = -1;
		while (!q.isEmpty()) {
			int u = q.poll();
			for (int h : adj[u]) {
				if(h!=pa[u])
				  pa[h]=u;
				if (a[h] == -1) {
					a[h] = 1 + a[u];
					q.add(h);
				}
			}
		}
		P = new int[n][m + 1];
		for (int i = 0; i < n; i++)
			Arrays.fill(P[i], -1);
		// base case: direct parents
		for (int i = 0; i < n; ++i)
			P[i][0] = pa[i];
		for(int j = 1; j <= m; j++)			
			for(int i = 0; i < n; i++)
				if(P[i][j-1] != -1)
					P[i][j] = P[P[i][j-1]][j-1];
		int hav=1;
		for (int i = n - 2; i >= 0; i--) {
			if (t[i])
				continue;
			int x=i;
			 for (int j = m; j >= 0; --j)
				 if (P[x][j]!=-1 && !t[P[x][j]])
					 x=P[x][j];
			int dest=a[i]-a[P[x][0]];
			if(dest+hav>n-k)
				continue;
			hav+=dest;
			x=i;
			t[i]=true;
			while(pa[x]!=-1 && !t[pa[x]]) {
				t[pa[x]]=true;
				x=pa[x];
			}
		}
		for (int i = 0; i < n; i++)
			if (!t[i])
				out.print((i + 1) + " ");
		out.flush();
	}
	static class qu implements Comparable<qu> {
		int a;
		int b;
		int w;

		qu(int aa, int bb, int cc) {
			a = aa;
			b = bb;
			w = cc;
		}

		public String toString() {
			return a + " " + b + " " + w;
		}

		public int compareTo(qu o) {
			if (a == o.a)
				return b - o.b;
			return a - o.a;
		}
	}

	static class seg implements Comparable<seg> {
		int a;
		int b;
		int l;
		int r;
		int bit;

		seg(int s, int e, int x, int y, int bi) {
			a = s;
			b = e;
			l = x;
			r = y;
			bit = bi;
		}

		public String toString() {
			return a + " " + b + " " + l + " " + r + " " + bit;
		}

		public int compareTo(seg o) {
			// if(a==o.a)
			return bit - o.bit;
			// return
		}
	}

	static class pair implements Comparable<pair> {
		long to;
		long number;

		pair(long t, long n) {
			number = n;
			to = t;
		}

		public String toString() {
			return to + " " + number;
		}

		@Override
		public int compareTo(pair o) {
			if (o.to < to)
				return 1;
			return -1;
		}

	}

	static long modPow(long a, int e)

	{
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a) % mod;
			a = (a * a) % mod;
			e >>= 1;
		}
		return res;
	}

	static long inver(long x) {
		long a = x;
		long e = (mod - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				res = ((1l * res * a) % mod);
			}
			a = ((1l * a * a) % mod);
			e >>= 1;
		}
		return res % mod;
	}

	static class edge implements Comparable<edge> {
		int from;
		int to;
		int number;

		edge(int f, int t, int n) {
			from = f;
			to = t;
			number = n;
		}

		public String toString() {
			return from + " " + to + " " + number;
		}

		public int compareTo(edge f) {
			return f.number - number;
		}
	}

	static void seive(int N) {
		si = new int[N];
		primes = new ArrayList<>();
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);
		}
	}

	static long fac(int n) {
		if (n == 0)
			return fac[n] = 1;
		if (n == 1)
			return fac[n] = 1;
		long ans = 1;
		for (int i = 1; i <= n; i++)
			fac[i] = ans = (i % mod * ans % mod) % mod;
		return ans % mod;
	}

	static long gcd(long a, long b) {

		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class unionfind {
		int[] p;
		int[] size;
		int[] max;
		int num;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];
			max = new int[n];
			for (int i = 0; i < n; i++) {
				p[i] = i;
				max[i] = i;
			}
			Arrays.fill(size, 1);
			num = n;
		}

		int findSet(int v) {
			if (v == p[v])
				return v;

			max[v] = Math.max(max[v], max[p[v]]);

			p[v] = findSet(p[v]);

			max[v] = Math.max(max[v], max[p[v]]);

			return p[v];
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		boolean combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			// System.out.println(num+" ppp");
			num--;
			if (size[a] > size[b]) {
				p[b] = a;
				max[a] = Math.max(max[a], max[b]);
				size[a] += size[b];

			} else {
				p[a] = b;
				max[b] = Math.max(max[a], max[b]);
				size[b] += size[a];
			}
			return false;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

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

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}