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 static java.lang.Integer.parseInt;
import static java.lang.Long.parseLong;
import static java.lang.System.arraycopy;
import static java.lang.System.exit;
import static java.util.Arrays.copyOf;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
import java.util.StringTokenizer;

public class C {

	static class IntList {

		int data[] = new int[3];
		int size = 0;

		boolean isEmpty() {
			return size == 0;
		}

		int size() {
			return size;
		}

		int get(int index) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			return data[index];
		}

		void clear() {
			size = 0;
		}

		void set(int index, int value) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			data[index] = value;
		}

		void expand() {
			if (size >= data.length) {
				data = copyOf(data, (data.length << 1) + 1);
			}
		}

		void insert(int index, int value) {
			if (index < 0 || index > size) {
				throw new IndexOutOfBoundsException();
			}
			expand();
			arraycopy(data, index, data, index + 1, size++ - index);
			data[index] = value;
		}

		int delete(int index) {
			if (index < 0 || index >= size) {
				throw new IndexOutOfBoundsException();
			}
			int value = data[index];
			arraycopy(data, index + 1, data, index, --size - index);
			return value;
		}

		void push(int value) {
			expand();
			data[size++] = value;
		}

		int pop() {
			if (size == 0) {
				throw new NoSuchElementException();
			}
			return data[--size];
		}

		void unshift(int value) {
			expand();
			arraycopy(data, 0, data, 1, size++);
			data[0] = value;
		}

		int shift() {
			if (size == 0) {
				throw new NoSuchElementException();
			}
			int value = data[0];
			arraycopy(data, 1, data, 0, --size);
			return value;
		}
	}

	static final int MOD = 1000000007;

	static int add(int a, int b) {
		int res = a + b;
		return res >= MOD ? res - MOD : res;
	}

	static int sub(int a, int b) {
		int res = a - b;
		return res < 0 ? res + MOD : res;
	}

	static int mul(int a, int b) {
		int res = (int) ((long) a * b % MOD);
		return res < 0 ? res + MOD : res;
	}

	static IntList edges[];
	static int m, k, x;

	static void solve() throws Exception {
		int n = scanInt();
		m = scanInt();
//		int n = 100000;
//		m = 1000000000;
		if (n < 1 || n > 100000 || m < 1 || m > 1000000000) {
			throw new AssertionError();
		}
		edges = new IntList[n];
		for (int i = 0; i < n; i++) {
			edges[i] = new IntList();
		}
		for (int i = 0; i < n - 1; i++) {
			int a = scanInt() - 1;
			int b = scanInt() - 1;
//			int a = i, b = i + 1;
			edges[a].push(b);
			edges[b].push(a);
		}
		k = scanInt() - 1;
		x = scanInt();
//		k = 500000000;
//		x = 10;
		if (k < 0 || k >= m || x < 1 || x > 10) {
			throw new AssertionError();
		}
		data = new int[3 * (x + 1) * (2 * n - 1)];
		free = 0;
		int res = dfs(0, -1);
		if (free != data.length) {
			throw new AssertionError();
		}
		int ans = 0;
		for (int i = 0; i <= x; i++) {
			ans = add(ans, data[res + i]);
		}
		out.print(ans);
	}

	static int data[], free;

	static int dfs(int cur, int prev) {
		int res = free; // <k, =k, >k
		free += 3 * (x + 1);
		data[res] = k;
		data[res + x + 2] = 1;
		data[res + 2 * x + 2] = m - k - 1;
		for (int i = 0; i < edges[cur].size; i++) {
			int next = edges[cur].get(i);
			if (next == prev) {
				continue;
			}
			int subres = dfs(next, cur); // all, <k, !=k
			int tmp = free;
			free += 3 * (x + 1);
			for (int ii = 0; ii < 3 * (x + 1); ii += x + 1) {
				for (int j = 0; j <= x; j++) {
					long v = 0;
					for (int jj = 0; jj <= j; jj++) {
						v += (long) data[res + ii + jj] * data[subres + ii + j - jj];
						v %= MOD;
					}
					data[tmp + ii + j] = (int) (v % MOD);
				}
			}
			res = tmp;
		}
		for (int i = 0; i <= x; i++) {
			int a = data[res + i], b = data[res + x + 1 + i], c = data[res + 2 * x + 2 + i];
//			a = mul(a, k);
//			c = mul(c, m - k - 1);
			c = add(a, c);
			data[res + i] = add(b, c);
			data[res + x + 1 + i] = a;
			data[res + 2 * x + 2 + i] = c;
		}
		return res;
	}

	static int scanInt() throws IOException {
		return parseInt(scanString());
	}

	static long scanLong() throws IOException {
		return parseLong(scanString());
	}

	static String scanString() throws IOException {
		while (tok == null || !tok.hasMoreTokens()) {
			tok = new StringTokenizer(in.readLine());
		}
		return tok.nextToken();
	}

	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer tok;

	public static void main(String[] args) {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			solve();
			in.close();
			out.close();
		} catch (Throwable e) {
			e.printStackTrace();
			exit(1);
		}
	}
}