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.*;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.HashMap;
import java.util.Map;

/**
 * Created by dalt on 2018/5/26.
 */
public class Contest480E {
    static final int INF = (int) 1e8;
    static final int MOD = (int) 1e9 + 7;
    public static BlockReader input;
    public static PrintStream output;
    public static Debug debug;

    public static void main(String[] args) throws FileNotFoundException {
        init();

        solve();

        destroy();
    }

    public static void init() throws FileNotFoundException {
        if (System.getProperty("ONLINE_JUDGE") == null) {
            input = new BlockReader(new FileInputStream("E:\\DATABASE\\TESTCASE\\codeforces\\Contest480E.in"));
            output = System.out;
        } else {
            input = new BlockReader(System.in);
            output = new PrintStream(new BufferedOutputStream(System.out), false);
        }

        debug = new Debug();
        debug.enter("main");
    }

    public static void solve() {
        int n = input.nextInteger();
        int k = input.nextInteger();
        int remain = n - k;

        LCTNode[] nodes = new LCTNode[n + 1];

        for (int i = 1; i <= n; i++) {
            nodes[i] = new LCTNode();
            nodes[i].id = i;
        }

        for (int i = 1; i < n; i++) {
            LCTNode a = nodes[input.nextInteger()];
            LCTNode b = nodes[input.nextInteger()];
            LCTNode.join(a, b);
        }

        int[] remove = new int[k];
        int removeLen = k;

        LCTNode root = nodes[n];
        LCTNode.makeRoot(root);
        for (int i = n; i >= 1; i--) {
            LCTNode.access(nodes[i]);
            LCTNode.splay(root);

            if (root.notIncludeNum > remain) {
                remove[--removeLen] = i;
                continue;
            }

            remain -= root.notIncludeNum;
            root.setInclude();
        }

        for (int i = 0; i < k; i++) {
            output.print(remove[i]);
            output.print(' ');
        }
    }

    public static void destroy() {
        output.flush();
        debug.exit();
        debug.statistic();
    }

    public static class LCTNode {
        public static final LCTNode NIL = new LCTNode();

        static {
            NIL.left = NIL;
            NIL.right = NIL;
            NIL.father = NIL;
            NIL.treeFather = NIL;
        }

        LCTNode left = NIL;
        LCTNode right = NIL;
        LCTNode father = NIL;
        LCTNode treeFather = NIL;
        boolean reverse;
        int id;

        boolean includeDirty;
        boolean include;
        int notIncludeNum;

        public static void access(LCTNode x) {
            LCTNode last = NIL;
            while (x != NIL) {
                splay(x);
                x.right.father = NIL;
                x.right.treeFather = x;
                x.setRight(last);
                x.pushUp();

                last = x;
                x = x.treeFather;
            }
        }

        public static void makeRoot(LCTNode x) {
            access(x);
            splay(x);
            x.reverse();
        }

        public static void cut(LCTNode y, LCTNode x) {
            makeRoot(y);
            access(x);
            splay(y);
            y.right.treeFather = NIL;
            y.right.father = NIL;
            y.setRight(NIL);
            y.pushUp();
        }

        public static void join(LCTNode y, LCTNode x) {
            makeRoot(x);
            x.treeFather = y;
        }

        public static void findRoute(LCTNode x, LCTNode y) {
            makeRoot(y);
            access(x);
        }

        public static void splay(LCTNode x) {
            if (x == NIL) {
                return;
            }
            LCTNode y, z;
            while ((y = x.father) != NIL) {
                if ((z = y.father) == NIL) {
                    y.pushDown();
                    x.pushDown();
                    if (x == y.left) {
                        zig(x);
                    } else {
                        zag(x);
                    }
                } else {
                    z.pushDown();
                    y.pushDown();
                    x.pushDown();
                    if (x == y.left) {
                        if (y == z.left) {
                            zig(y);
                            zig(x);
                        } else {
                            zig(x);
                            zag(x);
                        }
                    } else {
                        if (y == z.left) {
                            zag(x);
                            zig(x);
                        } else {
                            zag(y);
                            zag(x);
                        }
                    }
                }
            }

            x.pushDown();
            x.pushUp();
        }

        public static void zig(LCTNode x) {
            LCTNode y = x.father;
            LCTNode z = y.father;
            LCTNode b = x.right;

            y.setLeft(b);
            x.setRight(y);
            z.changeChild(y, x);

            y.pushUp();
        }

        public static void zag(LCTNode x) {
            LCTNode y = x.father;
            LCTNode z = y.father;
            LCTNode b = x.left;

            y.setRight(b);
            x.setLeft(y);
            z.changeChild(y, x);

            y.pushUp();
        }

        public static LCTNode findRoot(LCTNode x) {
            x.pushDown();
            while (x.left != NIL) {
                x = x.left;
                x.pushDown();
            }
            splay(x);
            return x;
        }

        public void setInclude() {
            this.include = true;
            includeDirty = true;
            notIncludeNum = 0;
        }

        @Override
        public String toString() {
            return "" + id;
        }

        public void pushDown() {
            if (reverse) {
                reverse = false;

                LCTNode tmpNode = left;
                left = right;
                right = tmpNode;

                left.reverse();
                right.reverse();
            }

            left.treeFather = treeFather;
            right.treeFather = treeFather;

            if (includeDirty) {
                left.setInclude();
                right.setInclude();
                includeDirty = false;
            }
        }

        public void reverse() {
            reverse = !reverse;
        }

        public void setLeft(LCTNode x) {
            left = x;
            x.father = this;
        }

        public void setRight(LCTNode x) {
            right = x;
            x.father = this;
        }

        public void changeChild(LCTNode y, LCTNode x) {
            if (left == y) {
                setLeft(x);
            } else {
                setRight(x);
            }
        }

        public void pushUp() {
            notIncludeNum = left.notIncludeNum + right.notIncludeNum;
            if (!include) {
                notIncludeNum += 1;
            }
        }
    }

    public static class Debug {
        boolean debug = System.getProperty("ONLINE_JUDGE") == null;
        Deque<ModuleRecorder> stack = new ArrayDeque<>();
        Map<String, Module> fragmentMap = new HashMap<>();

        public void enter(String module) {
            if (debug) {
                stack.push(new ModuleRecorder(getModule(module)));
            }
        }

        public Module getModule(String moduleName) {
            Module module = fragmentMap.get(moduleName);
            if (module == null) {
                module = new Module(moduleName);
                fragmentMap.put(moduleName, module);
            }
            return module;
        }

        public void exit() {
            if (debug) {
                ModuleRecorder fragment = stack.pop();
                fragment.exit();
            }
        }

        public void statistic() {
            if (!debug) {
                return;
            }

            if (stack.size() > 0) {
                throw new RuntimeException("Exist unexited tag");
            }
            System.out.println("\n------------------------------------------");

            System.out.println("memory used " + ((Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20) + "M");

            System.out.println("\n------------------------------------------");
            for (Module module : fragmentMap.values()) {
                System.out.println(String.format("Module %s : enter %d : cost %d", module.moduleName, module.enterTime, module.totaltime));
            }

            System.out.println("------------------------------------------");
        }

        public static class ModuleRecorder {
            Module fragment;
            long time;

            public ModuleRecorder(Module fragment) {
                this.fragment = fragment;
                time = System.currentTimeMillis();
            }

            public void exit() {
                fragment.totaltime += System.currentTimeMillis() - time;
                fragment.enterTime++;
            }
        }

        public static class Module {
            String moduleName;
            long totaltime;
            long enterTime;

            public Module(String moduleName) {
                this.moduleName = moduleName;
            }
        }
    }

    public static class BlockReader {
        static final int EOF = -1;
        InputStream is;
        byte[] dBuf;
        int dPos, dSize, next;
        StringBuilder builder = new StringBuilder();

        public BlockReader(InputStream is) {
            this(is, 8192);
        }

        public BlockReader(InputStream is, int bufSize) {
            this.is = is;
            dBuf = new byte[bufSize];
            next = nextByte();
        }

        public int nextByte() {
            while (dPos >= dSize) {
                if (dSize == -1) {
                    return EOF;
                }
                dPos = 0;
                try {
                    dSize = is.read(dBuf);
                } catch (Exception e) {
                }
            }
            return dBuf[dPos++];
        }

        public String nextBlock() {
            builder.setLength(0);
            skipBlank();
            while (next != EOF && !Character.isWhitespace(next)) {
                builder.append((char) next);
                next = nextByte();
            }
            return builder.toString();
        }

        public void skipBlank() {
            while (Character.isWhitespace(next)) {
                next = nextByte();
            }
        }

        public int nextInteger() {
            skipBlank();
            int ret = 0;
            boolean rev = false;
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = nextByte();
            }
            while (next >= '0' && next <= '9') {
                ret = (ret << 3) + (ret << 1) + next - '0';
                next = nextByte();
            }
            return rev ? -ret : ret;
        }

        public int nextBlock(char[] data, int offset) {
            skipBlank();
            int index = offset;
            int bound = data.length;
            while (next != EOF && index < bound && !Character.isWhitespace(next)) {
                data[index++] = (char) next;
                next = nextByte();
            }
            return index - offset;
        }

        public boolean hasMore() {
            skipBlank();
            return next != EOF;
        }
    }
}
