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.PrintWriter;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.Writer;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

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

    static class TaskC {
        static int[][] g;
        static int m;
        static int k;
        static int x;
        static final int MOD = 1000000007;
        static int[][][] dp;

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

        static int mul(int a, int b) {
            return (int) ((long) a * b % MOD);
        }

        static int any(int v, int e) {
            return add(add(dp[0][v][e], dp[1][v][e]), dp[2][v][e]);
        }

        static int less(int v, int e) {
            return dp[0][v][e];
        }

        static int nonequal(int v, int e) {
            return add(dp[0][v][e], dp[2][v][e]);
        }

        static void dfs(int v, int pv) {
            for (int to : g[v]) {
                if (to == pv) continue;
                dfs(to, v);
            }
            int[] less = new int[x + 1];
            less[0] = k - 1;
            int[] nless = new int[x + 1];
            int[] nequal = new int[x + 1];
            int[] ngreater = new int[x + 1];
            int[] equal = new int[x + 1];
            equal[1] = 1;
            int[] greater = new int[x + 1];
            greater[0] = m - k;
            for (int to : g[v]) {
                if (to == pv) continue;
                Arrays.fill(nless, 0);
                Arrays.fill(ngreater, 0);
                Arrays.fill(nequal, 0);
                for (int have = x; have >= 0; have--) {
                    int value = less[have];
                    if (value == 0) continue;
                    for (int get = 0; get + have <= x; get++) {
                        nless[get + have] = add(nless[get + have], mul(value, any(to, get)));
                    }
                }
                for (int have = x; have >= 0; have--) {
                    int value = equal[have];
                    if (value == 0) continue;
                    for (int get = 0; get + have <= x; get++) {
                        nequal[get + have] = add(nequal[get + have], mul(value, less(to, get)));
                    }
                }
                for (int have = x; have >= 0; have--) {
                    int value = greater[have];
                    if (value == 0) {
                        continue;
                    }
                    for (int get = 0; get + have <= x; get++) {
                        ngreater[get + have] = add(ngreater[get + have], mul(value, nonequal(to, get)));
                    }
                }
                {
                    int[] t = nequal;
                    nequal = equal;
                    equal = t;
                }
                {
                    int[] t = nless;
                    nless = less;
                    less = t;
                }
                {
                    int[] t = ngreater;
                    ngreater = greater;
                    greater = t;
                }
            }
            dp[0][v] = less;
            dp[1][v] = equal;
            dp[2][v] = greater;
        }

        public void solve(int testNumber, FastScanner in, FastPrinter out) {
            int n = in.nextInt();
            m = in.nextInt();
            int[] from = new int[n - 1];
            int[] to = new int[n - 1];
            for (int i = 0; i < n - 1; i++) {
                from[i] = in.nextInt() - 1;
                to[i] = in.nextInt() - 1;
            }
            g = GraphUtils.getEdgesUndirectedUnweighted(n, from, to);
            k = in.nextInt();
            x = in.nextInt();
            dp = new int[3][n][];
            dfs(0, -1);
            int ans = 0;
            for (int i = 0; i <= x; i++) {
                ans = add(ans, any(0, i));
            }
            out.println(ans);
        }

    }

    static class FastScanner extends BufferedReader {
        public FastScanner(InputStream is) {
            super(new InputStreamReader(is));
        }


        public int read() {
            try {
                int ret = super.read();
//            if (isEOF && ret < 0) {
//                throw new InputMismatchException();
//            }
//            isEOF = ret == -1;
                return ret;
            } catch (IOException e) {
                throw new InputMismatchException();
            }
        }

        static boolean isWhiteSpace(int c) {
            return c >= 0 && c <= 32;
        }

        public int nextInt() {
            int c = read();
            while (isWhiteSpace(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int ret = 0;
            while (c >= 0 && !isWhiteSpace(c)) {
                if (c < '0' || c > '9') {
                    throw new NumberFormatException("digit expected " + (char) c
                            + " found");
                }
                ret = ret * 10 + c - '0';
                c = read();
            }
            return ret * sgn;
        }

        public String readLine() {
            try {
                return super.readLine();
            } catch (IOException e) {
                return null;
            }
        }

    }

    static class GraphUtils {
        public static int[][] getEdgesUndirectedUnweighted(int n, int[] v, int[] u) {
            int[][] edges = new int[n][];
            int[] deg = getDegreeUndirected(n, v, u);
            for (int i = 0; i < n; i++) {
                edges[i] = new int[deg[i]];
            }
            int m = v.length;
            Arrays.fill(deg, 0);
            for (int i = 0; i < m; i++) {
                edges[v[i]][deg[v[i]]++] = u[i];
                edges[u[i]][deg[u[i]]++] = v[i];
            }
            return edges;
        }

        public static int[] getDegreeUndirected(int n, int[] v, int[] u) {
            int[] deg = new int[n];
            for (int i : v) {
                deg[i]++;
            }
            for (int i : u) {
                deg[i]++;
            }
            return deg;
        }

    }

    static class FastPrinter extends PrintWriter {
        public FastPrinter(OutputStream out) {
            super(out);
        }

        public FastPrinter(Writer out) {
            super(out);
        }

    }
}