Mashmokh is playing a new game. In the beginning he has k liters of water and p coins. Additionally he has a rooted tree (an undirected connected acyclic graph) that consists of m vertices. Each vertex of the tree contains a water tank that is empty in the beginning.

The game begins with the fact that Mashmokh chooses some (no more than k) of these tanks (except the root) and pours into each of them exactly 1 liter of water. Then the following process is performed until there is no water remained in tanks.

  * The process consists of several steps. 
  * At the beginning of each step Mashmokh opens doors of all tanks. Then Mashmokh closes doors of some tanks (he is not allowed to close door of tank in the root) for the duration of this move. Let's denote the number of liters in some tank with closed door as w, Mashmokh pays w coins for the closing of that tank during this move. 
  * Let's denote by x1, x2, ..., xm as the list of vertices of the tree sorted (nondecreasing) by their depth. The vertices from this list should be considered one by one in the order. Firstly vertex x1 (which is the root itself) is emptied. Then for each vertex xi (i > 1), if its door is closed then skip the vertex else move all the water from the tank of vertex xi to the tank of its father (even if the tank of the father is closed). 



Suppose l moves were made until the tree became empty. Let's denote the amount of water inside the tank of the root after the i-th move by wi then Mashmokh will win max(w1, w2, ..., wl) dollars. Mashmokh wanted to know what is the maximum amount of dollars he can win by playing the above game. He asked you to find this value for him.

Input

The first line of the input contains three space-separated integers m, k, p (2 ≤ m ≤ 105; 0 ≤ k, p ≤ 109). 

Each of the following m - 1 lines contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ m; ai ≠ bi) — the edges of the tree.

Consider that the vertices of the tree are numbered from 1 to m. The root of the tree has number 1.

Output

Output a single integer, the number Mashmokh asked you to find.

Examples

Input

10 2 1
1 2
1 3
3 4
3 5
2 6
6 8
6 7
9 8
8 10


Output

2


Input

5 1000 1000
1 2
1 3
3 4
3 5


Output

4

Note

The tree in the first sample is shown on the picture below. The black, red, blue colors correspond to vertices with 0, 1, 2 liters of water.

<image>

One way to achieve the maximum amount of money is to put 1 liter of water in each of vertices 3 and 4. The beginning state is shown on the picture below.

<image>

Then in the first move Mashmokh will pay one token to close the door of the third vertex tank. The tree after the first move is shown on the picture below.

<image>

After the second move there are 2 liters of water in the root as shown on the picture below.

<image>
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DMashmokhAndWaterTanks solver = new DMashmokhAndWaterTanks();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DMashmokhAndWaterTanks {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int m = in.ri();
            int k = in.ri();
            int p = in.ri();
            Node[] nodes = new Node[m];
            for (int i = 0; i < m; i++) {
                nodes[i] = new Node();
            }
            for (int i = 0; i < m - 1; i++) {
                Node a = nodes[in.ri() - 1];
                Node b = nodes[in.ri() - 1];
                a.adj.add(b);
                b.adj.add(a);
            }
            dfs(nodes[0], null);
            int[] cnt = new int[m];
            for (Node node : nodes) {
                cnt[node.depth]++;
            }
            cnt[0] = 0;
            Segment st = new Segment(0, m - 1, i -> cnt[i]);
            Query query = new Query();
            long best = 0;
            for (int i = 0; i < m; i++) {
                query.clear(p);
                st.update(0, i - 1, 0, m - 1, 1);
                st.query(0, i, 0, m - 1, query);
                best = Math.max(best, query.size);
            }
            best = Math.min(best, k);
            out.println(best);
        }

        public void dfs(Node root, Node p) {
            root.depth = p == null ? 0 : p.depth + 1;
            for (Node node : root.adj) {
                if (node == p) {
                    continue;
                }
                dfs(node, root);
            }
        }

    }

    static class Node {
        List<Node> adj = new ArrayList<>();
        int depth;

    }

    static class DigitUtils {
        private DigitUtils() {
        }

        public static int floorAverage(int x, int y) {
            return (x & y) + ((x ^ y) >> 1);
        }

    }

    static interface IntToIntegerFunction {
        int apply(int x);

    }

    static class Query {
        int k;
        int size;
        boolean hasMore;

        public void clear(int k) {
            this.k = k;
            size = 0;
            hasMore = true;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println(long c) {
            return append(c).println();
        }

        public FastOutput println() {
            return append('\n');
        }

        public FastOutput flush() {
            try {
//            boolean success = false;
//            if (stringBuilderValueField != null) {
//                try {
//                    char[] value = (char[]) stringBuilderValueField.get(cache);
//                    os.write(value, 0, cache.length());
//                    success = true;
//                } catch (Exception e) {
//                }
//            }
//            if (!success) {
                os.append(cache);
//            }
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int ri() {
            return readInt();
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Segment implements Cloneable {
        private Segment left;
        private Segment right;
        private int size;
        private long totalCost;
        private int unitCost;

        private void modify(int x) {
            unitCost += x;
            totalCost += (long) size * x;
        }

        public void pushUp() {
            size = left.size + right.size;
            totalCost = left.totalCost + right.totalCost;
        }

        public void pushDown() {
            if (unitCost != 0) {
                left.modify(unitCost);
                right.modify(unitCost);
                unitCost = 0;
            }
        }

        public Segment(int l, int r, IntToIntegerFunction func) {
            if (l < r) {
                int m = DigitUtils.floorAverage(l, r);
                left = new Segment(l, m, func);
                right = new Segment(m + 1, r, func);
                pushUp();
            } else {
                size = func.apply(l);
            }
        }

        private boolean enter(int L, int R, int l, int r) {
            return L <= l && R >= r;
        }

        private boolean leave(int L, int R, int l, int r) {
            return L > r || R < l;
        }

        public void update(int L, int R, int l, int r, int x) {
            if (leave(L, R, l, r)) {
                return;
            }
            if (enter(L, R, l, r)) {
                modify(x);
                return;
            }
            pushDown();
            int m = DigitUtils.floorAverage(l, r);
            left.update(L, R, l, m, x);
            right.update(L, R, m + 1, r, x);
            pushUp();
        }

        public void query(int L, int R, int l, int r, Query q) {
            if (leave(L, R, l, r) || !q.hasMore) {
                return;
            }
            if (enter(L, R, l, r)) {
                if (q.k >= totalCost) {
                    q.k -= totalCost;
                    q.size += size;
                    return;
                }

                if (l == r) {
                    q.size += q.k / unitCost;
                    q.k %= unitCost;
                    q.hasMore = false;
                    return;
                }
            }
            pushDown();
            int m = DigitUtils.floorAverage(l, r);
            right.query(L, R, m + 1, r, q);
            left.query(L, R, l, m, q);
        }

        private Segment deepClone() {
            Segment seg = clone();
            if (seg.left != null) {
                seg.left = seg.left.deepClone();
            }
            if (seg.right != null) {
                seg.right = seg.right.deepClone();
            }
            return seg;
        }

        protected Segment clone() {
            try {
                return (Segment) super.clone();
            } catch (CloneNotSupportedException e) {
                throw new RuntimeException(e);
            }
        }

        private void toString(StringBuilder builder) {
            if (left == null && right == null) {
                builder.append("val").append(",");
                return;
            }
            pushDown();
            left.toString(builder);
            right.toString(builder);
        }

        public String toString() {
            StringBuilder builder = new StringBuilder();
            deepClone().toString(builder);
            if (builder.length() > 0) {
                builder.setLength(builder.length() - 1);
            }
            return builder.toString();
        }

    }
}

