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.io.BufferedInputStream;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Arrays;

public class E6 {
	/*
1 2 3 5 6 7 8 9 10 11 12 14 
	 */
	public static void main(String[] args) {
		JS in = new JS();
		PrintWriter out = new PrintWriter(System.out);
		int N = in.nextInt();
		int K = in.nextInt();
		int count[] = new int[N];
		int input[] = new int[2*N-2];
		//Read in input to make adj a double array
		for(int i = 0; i < N-1; i++) {
			int v1 = in.nextInt()-1;
			int v2 = in.nextInt()-1;
			count[v1]++;
			count[v2]++;
			input[2*i]=v1;
			input[2*i+1]=v2;
		}
		//Go through the input and set the adj array
		int adj[][] = new int[N][];
		for(int i = 0; i < N; i++) adj[i] = new int[count[i]];
		count = null;
		int curOn[] = new int[N];
		for(int i = 0; i < N-1; i++) {
			int v1 = input[2*i];
			int v2 = input[2*i+1];
			adj[v1][curOn[v1]]=v2;
			adj[v2][curOn[v2]]=v1;
			curOn[v1]++;
			curOn[v2]++;
		}
		
		int [][]lift = new int[N][];	
		int []maxLog = new int[N];
		int []dep = new int[N];

		//Create tree
		lift[N-1] = new int[2];
		lift[N-1][0] = -1;
		lift[N-1][1] = -1;
		maxLog[N-1] = 1;
		ArrayDeque<Integer> nodeQ = new ArrayDeque<Integer>();
		ArrayDeque<Integer> prevQ = new ArrayDeque<Integer>();
		ArrayDeque<Integer> depQ = new ArrayDeque<Integer>();
		for(Integer next : adj[N-1]) {
			nodeQ.add(next);
			prevQ.add(N-1);
			depQ.add(1);
		}
		
		while(!nodeQ.isEmpty()) {
			int node = nodeQ.poll();
			int prev = prevQ.poll();
			int depp = depQ.poll();
			//Dynamicly allocate array space to save space
			int log = 31-Integer.numberOfLeadingZeros(depp)+2;
			lift[node] = new int[log];
			Arrays.fill(lift[node], -1);
			lift[node][0] = prev;
			dep[node] = depp;
			int curNode = prev; //Currently on our parent node
			for(int i = 1;; i++) {
				//If we want to go up 8, then we just go up 4 twice. We are already up 4 from
				//previous calculation, so check lift[node][4] for current
				//If it's greater than array length or equal to 0 (not initialized
				//then we know that we exceeded the height of the tree so set it to the root
				if(i-1 >= lift[curNode].length || lift[curNode][i-1] < 0) curNode = N-1;
				else curNode = lift[curNode][i-1];
				lift[node][i] = curNode;
				maxLog[node] = i;
				if(curNode == N-1 || curNode == -1) break;
			}
			for(Integer next : adj[node]) {
				if(next != prev) {
					nodeQ.add(next);
					prevQ.add(node);
					depQ.add(depp+1);
				}
			}
		}
		
		boolean []used = new boolean[N];
		used[N-1] = true;
		int canTake = N-1-K;
		
		for(int i = N-2; i >= 0; i--) { //If we can take this node, greedily do it
			//Get highest parent node that's node used
			if(used[i])continue;			
			int curNode = i;

			for(int jump = maxLog[curNode]; jump >= 0; jump--) {
				if(jump > maxLog[curNode])continue;
				if(!used[lift[curNode][jump]]) curNode = lift[curNode][jump];
			}

					
			int taking = dep[i]-dep[lift[curNode][0]];
			if(taking <= canTake) {
				canTake -= taking;
				int cur = i;
				while(true) {
					if(used[cur])break;
					used[cur] = true;
					cur = lift[cur][0];
				}
				if(canTake == 0) break;
			}
			
		}
		
		for(int i = 0; i < N-1; i++) {
			if(!used[i]) out.print((i+1)+" ");
		}
		out.close();
		
	}


	
	static class JS{
		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 JS() {
			in = new BufferedInputStream(System.in, BS);
		}
		
		public JS(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;
			}
		}
	}
	
}
