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.util.function.IntConsumer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jialin Ouyang (Jialin.Ouyang@gmail.com)
 */
public class Main {
  public static void main(String[] args) {
    InputStream inputStream = System.in;
    OutputStream outputStream = System.out;
    QuickScanner in = new QuickScanner(inputStream);
    QuickWriter out = new QuickWriter(outputStream);
    TaskC solver = new TaskC();
    solver.solve(1, in, out);
    out.close();
  }

  static class TaskC {
    static IntModular MOD = new IntModular();
    int vertexCnt;
    int typeCnt;
    int kType;
    int kCnt;
    Tree tree;
    int[][] less;
    int[][] equal;
    int[][] greater;
    int[][] tmpLess;
    int[][] tmpEqual;
    int[][] tmpGreater;

    public void solve(int testNumber, QuickScanner in, QuickWriter out) {
      vertexCnt = in.nextInt();
      typeCnt = in.nextInt();
      tree = new Tree(vertexCnt);
      tree.init(vertexCnt);
      for (int i = 1; i < vertexCnt; ++i) {
        tree.add(in.nextInt() - 1, in.nextInt() - 1);
      }
      kType = in.nextInt();
      kCnt = in.nextInt();
      less = new int[kCnt + 1][vertexCnt];
      equal = new int[kCnt + 1][vertexCnt];
      greater = new int[kCnt + 1][vertexCnt];
      tmpLess = new int[2][kCnt + 1];
      tmpEqual = new int[2][kCnt + 1];
      tmpGreater = new int[2][kCnt + 1];
      dfs(0, -1);
      int res = 0;
      for (int cnt = 0; cnt <= kCnt; ++cnt) {
        res = MOD.add(MOD.add(MOD.add(
            res,
            less[cnt][0]),
            equal[cnt][0]),
            greater[cnt][0]);
      }
      out.println(res);
    }

    void dfs(int u, int parent) {
      tree.forEachOutNodes(u, v -> {
        if (v != parent) dfs(v, u);
      });
      int t = 0;
      Arrays.fill(tmpLess[t], 0);
      tmpLess[t][0] = kType - 1;
      Arrays.fill(tmpEqual[t], 0);
      tmpEqual[t][1] = 1;
      Arrays.fill(tmpGreater[t], 0);
      tmpGreater[t][0] = typeCnt - kType;
      for (int edgeIdx = tree.lastOut(u); edgeIdx >= 0; edgeIdx = tree.nextOut(edgeIdx)) {
        int v = tree.toIdx(edgeIdx);
        if (v == parent) continue;
        Arrays.fill(tmpLess[t ^ 1], 0);
        Arrays.fill(tmpEqual[t ^ 1], 0);
        Arrays.fill(tmpGreater[t ^ 1], 0);
        for (int oldCnt = 0; oldCnt <= kCnt; ++oldCnt) {
          for (int delta = 0, newCnt = oldCnt; newCnt <= kCnt; ++delta, ++newCnt) {
            tmpLess[t ^ 1][newCnt] = MOD.add(
                tmpLess[t ^ 1][newCnt],
                MOD.mul(
                    tmpLess[t][oldCnt],
                    MOD.add(MOD.add(
                        less[delta][v],
                        equal[delta][v]),
                        greater[delta][v])));
            tmpEqual[t ^ 1][newCnt] = MOD.add(
                tmpEqual[t ^ 1][newCnt],
                MOD.mul(
                    tmpEqual[t][oldCnt],
                    less[delta][v]));
            tmpGreater[t ^ 1][newCnt] = MOD.add(
                tmpGreater[t ^ 1][newCnt],
                MOD.mul(
                    tmpGreater[t][oldCnt],
                    MOD.add(
                        less[delta][v],
                        greater[delta][v])));
          }
        }
        t ^= 1;
      }
      for (int cnt = 0; cnt <= kCnt; ++cnt) {
        less[cnt][u] = tmpLess[t][cnt];
        equal[cnt][u] = tmpEqual[t][cnt];
        greater[cnt][u] = tmpGreater[t][cnt];
      }
    }

  }

  static class IntModular {
    private static final int MOD = 1000000007;
    public final int mod;
    private final int[] x;

    public IntModular() {
      this(MOD);
    }

    public IntModular(int mod) {
      this.mod = mod;
      this.x = new int[2];
    }

    public int add(int a, int b) {
      return fix(a + b);
    }

    public int fix(int a) {
      a = slightFix(a);
      return 0 <= a && a < mod ? a : slightFix(a % mod);
    }

    public int mul(int a, int b) {
      return a > 0
          ? (b < mod / a ? a * b : (int) ((long) a * b % mod))
          : 0;
    }

    private int slightFix(int a) {
      return a >= mod
          ? a - mod
          : a < 0 ? a + mod : a;
    }

  }

  static class QuickScanner {
    private static final int BUFFER_SIZE = 1024;
    private InputStream stream;
    private byte[] buffer;
    private int currentPosition;
    private int numberOfChars;

    public QuickScanner(InputStream stream) {
      this.stream = stream;
      this.buffer = new byte[BUFFER_SIZE];
      this.currentPosition = 0;
      this.numberOfChars = 0;
    }

    public int nextInt() {
      int c = nextNonSpaceChar();
      boolean positive = true;
      if (c == '-') {
        positive = false;
        c = nextChar();
      }
      int res = 0;
      do {
        if (c < '0' || '9' < c) throw new RuntimeException();
        res = res * 10 + c - '0';
        c = nextChar();
      } while (!isSpaceChar(c));
      return positive ? res : -res;
    }

    public int nextNonSpaceChar() {
      int res = nextChar();
      for (; isSpaceChar(res) || res < 0; res = nextChar()) ;
      return res;
    }

    public int nextChar() {
      if (numberOfChars == -1) {
        throw new RuntimeException();
      }
      if (currentPosition >= numberOfChars) {
        currentPosition = 0;
        try {
          numberOfChars = stream.read(buffer);
        } catch (Exception e) {
          throw new RuntimeException(e);
        }
        if (numberOfChars <= 0) {
          return -1;
        }
      }
      return buffer[currentPosition++];
    }

    public boolean isSpaceChar(int c) {
      return c == ' ' || c == '\t' || isEndOfLineChar(c);
    }

    public boolean isEndOfLineChar(int c) {
      return c == '\n' || c == '\r' || c < 0;
    }

  }

  static abstract class AbstractBidirectionalGraph extends AbstractDirectedGraph implements BidirectionalGraphInterface {
    public AbstractBidirectionalGraph() {
      super();
    }

    public AbstractBidirectionalGraph(int vertexCapacity, int edgeCapacity) {
      super(vertexCapacity, edgeCapacity << 1);
    }

    public AbstractBidirectionalGraph(int vertexCapacity, int edgeCapacity, boolean initialize) {
      super(vertexCapacity, edgeCapacity << 1, initialize);
    }


    public void add(int u, int v) {
      super.add(u, v);
      super.add(v, u);
    }

  }

  static interface TreeInterface extends BidirectionalGraphInterface {
  }

  static abstract class AbstractDirectedGraph implements DirectedGraphInterface {
    protected int vertexCnt;
    protected int currentEdgeCnt;
    protected int[] fromIdx;
    protected int[] toIdx;
    protected int[] nextIn;
    protected int[] nextOut;
    protected int[] lastIn;
    protected int[] lastOut;
    protected int[] inDegree;
    protected int[] outDegree;

    public abstract void createVertexStorage(int vertexCapacity);

    public abstract void expandEdgeStorage(int edgeCapacity);

    public abstract void initVertexStorage(int vertexCnt);

    public AbstractDirectedGraph() {
    }

    public AbstractDirectedGraph(int vertexCapacity, int edgeCapacity) {
      this(vertexCapacity, edgeCapacity, true);
    }

    public AbstractDirectedGraph(int vertexCapacity, int edgeCapacity, boolean initialize) {
      ensureVertexCapacity(vertexCapacity);
      ensureEdgeCapacity(edgeCapacity);
      if (initialize) init(vertexCapacity);
    }


    public void init(int vertexCnt) {
      ensureVertexCapacity(vertexCnt);
      this.vertexCnt = vertexCnt;
      currentEdgeCnt = 0;
      Arrays.fill(inDegree, 0, vertexCnt, 0);
      Arrays.fill(outDegree, 0, vertexCnt, 0);
      Arrays.fill(lastIn, 0, vertexCnt, -1);
      Arrays.fill(lastOut, 0, vertexCnt, -1);
      initVertexStorage(vertexCnt);
    }


    public void add(int fromIdx, int toIdx) {
      ensureEdgeCapacity(currentEdgeCnt + 1);
      this.fromIdx[currentEdgeCnt] = fromIdx;
      this.toIdx[currentEdgeCnt] = toIdx;
      ++outDegree[fromIdx];
      ++inDegree[toIdx];
      nextOut[currentEdgeCnt] = lastOut[fromIdx];
      lastOut[fromIdx] = currentEdgeCnt;
      nextIn[currentEdgeCnt] = lastIn[toIdx];
      lastIn[toIdx] = currentEdgeCnt;
      ++currentEdgeCnt;
    }


    public int toIdx(int edgeIdx) {
      return toIdx[edgeIdx];
    }


    public int lastOut(int nodeIdx) {
      return lastOut[nodeIdx];
    }


    public int nextOut(int edgeIdx) {
      return nextOut[edgeIdx];
    }


    public void forEachOutNodes(int nodeIdx, IntConsumer consumer) {
      for (int edgeIdx = lastOut[nodeIdx]; edgeIdx >= 0; edgeIdx = nextOut[edgeIdx]) {
        consumer.accept(toIdx[edgeIdx]);
      }
    }

    private void ensureVertexCapacity(int vertexCapacity) {
      if (lastIn != null && lastIn.length >= vertexCapacity) return;
      int capacity = IntUtils.nextPow2(vertexCapacity);
      lastIn = new int[capacity];
      lastOut = new int[capacity];
      inDegree = new int[capacity];
      outDegree = new int[capacity];
      createVertexStorage(capacity);
    }

    private void ensureEdgeCapacity(int edgeCapacity) {
      if (fromIdx != null && fromIdx.length >= edgeCapacity) return;
      int capacity = IntUtils.nextPow2(edgeCapacity);
      fromIdx = IntArrayUtils.expand(fromIdx, capacity);
      toIdx = IntArrayUtils.expand(toIdx, capacity);
      nextIn = IntArrayUtils.expand(nextIn, capacity);
      nextOut = IntArrayUtils.expand(nextOut, capacity);
      expandEdgeStorage(capacity);
    }

  }

  static class Tree extends AbstractTree {
    public Tree(int vertexCapacity) {
      super(vertexCapacity);
    }


    public void createVertexStorage(int vertexCapacity) {
    }


    public void expandEdgeStorage(int edgeCapacity) {
    }


    public void initVertexStorage(int vertexCnt) {
    }

  }

  static abstract class AbstractTree extends AbstractBidirectionalGraph implements TreeInterface {
    public AbstractTree(int vertexCapacity) {
      super(vertexCapacity, vertexCapacity - 1);
    }

  }

  static class IntUtils {
    public static boolean isPow2(int n) {
      return n > 0 && (n & (n - 1)) == 0;
    }

    public static int nextPow2(int n) {
      if (n < 1) return 1;
      return isPow2(n) ? n : Integer.highestOneBit(n) << 1;
    }

  }

  static interface DirectedGraphInterface {
  }

  static class IntArrayUtils {
    public static int[] expand(int[] values, int newLength) {
      if (values != null && values.length >= newLength) return values;
      int[] res = new int[newLength];
      if (values == null) return res;
      for (int i = 0; i < values.length; ++i) res[i] = values[i];
      return res;
    }

  }

  static interface BidirectionalGraphInterface extends DirectedGraphInterface {
  }

  static class QuickWriter {
    private final PrintWriter writer;

    public QuickWriter(OutputStream outputStream) {
      this.writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

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

    public void print(Object... objects) {
      for (int i = 0; i < objects.length; ++i) {
        if (i > 0) {
          writer.print(' ');
        }
        writer.print(objects[i]);
      }
    }

    public void println(Object... objects) {
      print(objects);
      writer.print('\n');
    }

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

  }
}