Problem: Harry, Ron and Hermione have figured out that Helga Hufflepuff's cup is a horcrux. Through her encounter with Bellatrix Lestrange, Hermione came to know that the cup is present in Bellatrix's family vault in Gringott's Wizarding Bank. 

The Wizarding bank is in the form of a tree with total n vaults where each vault has some type, denoted by a number between 1 to m. A tree is an undirected connected graph with no cycles.

The vaults with the highest security are of type k, and all vaults of type k have the highest security.

There can be at most x vaults of highest security. 

Also, if a vault is of the highest security, its adjacent vaults are guaranteed to not be of the highest security and their type is guaranteed to be less than k.

Harry wants to consider every possibility so that he can easily find the best path to reach Bellatrix's vault. So, you have to tell him, given the tree structure of Gringotts, the number of possible ways of giving each vault a type such that the above conditions hold.

Input

The first line of input contains two space separated integers, n and m — the number of vaults and the number of different vault types possible. (1 ≤ n ≤ 105, 1 ≤ m ≤ 109).

Each of the next n - 1 lines contain two space separated integers ui and vi (1 ≤ ui, vi ≤ n) representing the i-th edge, which shows there is a path between the two vaults ui and vi. It is guaranteed that the given graph is a tree.

The last line of input contains two integers k and x (1 ≤ k ≤ m, 1 ≤ x ≤ 10), the type of the highest security vault and the maximum possible number of vaults of highest security.

Output

Output a single integer, the number of ways of giving each vault a type following the conditions modulo 109 + 7.

Examples

Input

4 2
1 2
2 3
1 4
1 2


Output

1


Input

3 3
1 2
1 3
2 1


Output

13


Input

3 1
1 2
1 3
1 1


Output

0

Note

In test case 1, we cannot have any vault of the highest security as its type is 1 implying that its adjacent vaults would have to have a vault type less than 1, which is not allowed. Thus, there is only one possible combination, in which all the vaults have type 2.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.ArrayList;
import java.io.InputStream;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC {
        int normalMultiplier;
        int extraMultiplier;
        int x;

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            int n = in.readInt();
            int m = in.readInt(); // range of vault types
            Node[] nodes = new Node[n];
            for (int i = 0; i < nodes.length; i++) {
                nodes[i] = new Node(i);
            }
            for (int i = 0; i < nodes.length - 1; i++) {
                int u = in.readInt() - 1;
                int v = in.readInt() - 1;
                nodes[u].adj.add(nodes[v]);
                nodes[v].adj.add(nodes[u]);
            }
            int k = in.readInt(); // type of highest security vault
            x = in.readInt(); // max number of vaults of highest security
            normalMultiplier = k - 1;
            extraMultiplier = m - normalMultiplier - 1;
            long res = 0;
            for (int exactly = 0; exactly <= x; exactly++) {
                int temp = nodes[0].ways(null, exactly, 2);
                res += temp;
            }
            out.printLine(res % MiscUtils.MOD7);
        }

        class Node {
            int index;
            ArrayList<Node> adj = new ArrayList<>();
            Node parent;
            int[] waysmem;
            int[][] cache;

            public Node(int index) {
                this.index = index;
            }

            int ways(Node parent, int exactly, int queryType) {
                if (waysmem == null) {
                    waysmem = new int[3 * (x + 1)];
                    Arrays.fill(waysmem, -1);
                }
                int index = 3 * exactly + queryType;
                if (waysmem[index] != -1) {
                    return waysmem[index];
                }
                this.parent = parent;
                int res = 0;
                { // for all types we have option of it not being special
                    res += ((long) normalMultiplier * solveChildren(2, exactly)) % MiscUtils.MOD7;
                    res %= MiscUtils.MOD7;
                }
                if (queryType >= 1) { // extra multiplier possible if parent and children not special
                    res += ((long) extraMultiplier * solveChildren(1, exactly)) % MiscUtils.MOD7;
                    res %= MiscUtils.MOD7;
                }
                if (queryType == 2 && exactly > 0) { // have it be special
                    res += solveChildren(0, exactly - 1);
                    res %= MiscUtils.MOD7;
                }
                return waysmem[index] = res;
            }

            int solveChildren(int queryType, int exactly) {
                if (cache == null) {
                    cache = new int[3][];
                }
                if (cache[queryType] == null) {
                    solveChildrenHelper(queryType);
                }
                return cache[queryType][exactly];
            }

            void solveChildrenHelper(int queryType) {
                int[][] mem = new int[adj.size() + 1][x + 1];
                for (int index = adj.size(); index >= 0; index--) {
                    for (int exactly = 0; exactly <= x; exactly++) {
                        if (index == adj.size()) {
                            mem[index][exactly] = (exactly == 0 ? 1 : 0);
                        } else if (adj.get(index) == parent) {
                            mem[index][exactly] = mem[index + 1][exactly];
                        } else {
                            int res = 0;
                            for (int subtreeExact = 0; subtreeExact <= exactly; subtreeExact++) {
                                res += ((long) adj.get(index).ways(this, subtreeExact, queryType) * mem[index + 1][exactly - subtreeExact]) % MiscUtils.MOD7;
                                res %= MiscUtils.MOD7;
                            }
                            mem[index][exactly] = res;
                        }
                    }
                }
                cache[queryType] = mem[0];
            }
        }
    }
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    static class MiscUtils {
        public static final int MOD7 = (int) (1e9 + 7);
    }
    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void close() {
            writer.close();
        }

        public void printLine(long i) {
            writer.println(i);
        }
    }
}