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 sun.dc.pr.PRError;

import java.io.*;
import java.util.*;

public class Solution {


    static MyScanner sc;
    private static PrintWriter out;
    static long M = 1000000007;


    public static void main(String[] s) throws Exception {
        StringBuilder stringBuilder = new StringBuilder();
//
//        stringBuilder.append("5 9\n" +
//                "mahmoud mahmoudbadawy drmahmoud drevil mahmoud\n" +
//                "1 1 5\n" +
//                "1 1 2\n" +
//                "1 2 3\n" +
//                "2 3 mahmoud\n" +
//                "2 4 mahmoud\n" +
//                "2 2 mahmouu\n" +
//                "1 1 5\n" +
//                "1 2 3\n" +
//                "1 1 1\n");


        if (stringBuilder.length() == 0) {
            sc = new MyScanner(System.in);
        } else {
            sc = new MyScanner(new BufferedReader(new StringReader(stringBuilder.toString())));
        }

        out = new PrintWriter(new OutputStreamWriter(System.out));

        initData();
        solve();
        out.flush();
    }


    private static void initData() {
    }

    private static ArrayList<int[]> safe = new ArrayList<>();

    private static void solve() throws IOException {
        int n = sc.nextInt();
        int m = sc.nextInt();
        HashSet<Integer>[] fff = new HashSet[n];
        for (int i = 0; i < n; i++) {
            fff[i] = new HashSet<>();
        }
        for (int i = 0; i < n - 1; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            fff[a].add(b);
            fff[b].add(a);
        }
        int k = sc.nextInt();
        int x = sc.nextInt();
        long[][][] rt = new long[n][3][x + 1];
        for (int i = 0; i < n; i++) {
            rt[i][0][0] = k - 1;
            rt[i][1][1] = 1;
            rt[i][2][0] = m - k;
        }
        int last = 0;
        for (int i = 0; i < n; i++) {
            int cur = i;
            while (fff[cur].size() == 1) {
                int next = fff[cur].iterator().next();
                fff[cur].remove(next);
                last = next;
                fff[next].remove(cur);
                long[][] old = rt[next];
                rt[next] = new long[3][x + 1];
                // min

                for (int m1 = 0; m1 <= x; m1++) {
                    for (int m2 = 0; m2 <= x; m2++) {
                        if (m1 + m2 > x) break;
                        rt[next][0][m1 + m2] += old[0][m1] * ((rt[cur][1][m2] + rt[cur][0][m2] + rt[cur][2][m2]) % M);
                        rt[next][1][m1 + m2] += old[1][m1] * (rt[cur][0][m2]);
                        rt[next][2][m1 + m2] += old[2][m1] * ((rt[cur][0][m2] + rt[cur][2][m2])% M);


                        rt[next][0][m1 + m2] %= M;
                        rt[next][1][m1 + m2] %= M;
                        rt[next][2][m1 + m2] %= M;
                    }


                }
                cur = next;
            }
        }

//        System.out.println(Arrays.deepToString(rt));
        long res = 0;
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j <= x; j++) {
                res += rt[last][i][j];
                if (res > M) res -= M;
            }
        }

        out.println(res);
    }


    private static int[][] tr(int n) {
        int[][] x = new int[2][n - 1];
        for (int i = 0; i < n - 1; i++) {
            x[0][i] = sc.nextInt() - 1;
            x[1][i] = sc.nextInt() - 1;
        }
        int[][] neig = pn(x, n);
        return neig;
    }

    private static int[][] pn(int[][] x, int n) {
        int[] ct = new int[n];
        int[][] res = new int[n][];
        for (int v : x[0]) {
            ct[v]++;
        }
        for (int v : x[1]) {
            ct[v]++;
        }
        for (int l = 0; l < n; l++) {
            res[l] = new int[ct[l]];
        }
        for (int i = 0; i < x[0].length; i++) {
            res[x[0][i]][--ct[x[0][i]]] = x[1][i];
            res[x[1][i]][--ct[x[1][i]]] = x[0][i];
        }
        return res;
    }


    private static long crt(long a1, long a2, long n1, long n2) {
        long[] ex = extEucl(n1, n2);
        long p = (a1 * n2 * ex[1] + a2 * n1 * ex[0]) % (n2 * n1);
        if (p < 0) p += n1 * n2;
        return p;
    }

    private static long[] extEucl(long a, long b) {
        long r0 = a, r1 = b, s0 = 1, s1 = 0, t0 = 0, t1 = 1;
        while (r1 != 0) {
            long k = r0 / r1;
            long rt = r1;
            r1 = r0 - k * r1;
            r0 = rt;

            long st = s1;
            s1 = s0 - k * s1;
            s0 = st;

            long tt = t1;
            t1 = t0 - k * t1;
            t0 = tt;

        }
        return new long[]{s0, t0};
    }


    private static void solveT() throws IOException {
        int t = sc.nextInt();
        while (t-- > 0) {
            solve();
        }
    }


    private static long gcd(long l, long l1) {
        if (l > l1) return gcd(l1, l);
        if (l == 0) return l1;
        return gcd(l1 % l, l);
    }

    private static long pow(long a, long b, long m) {
        if (b == 0) return 1;
        if (b == 1) return a;
        long pp = pow(a, b / 2, m);
        pp *= pp;
        pp %= m;
        return (pp * (b % 2 == 0 ? 1 : a)) % m;
    }


    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        MyScanner(BufferedReader br) {
            this.br = br;
        }

        public MyScanner(InputStream in) {
            this(new BufferedReader(new InputStreamReader(in)));
        }

        void findToken() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
        }

        String next() {
            findToken();
            return st.nextToken();
        }

        Integer[] nab(int n) {
            Integer[] k = new Integer[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        int[] na(int n) {
            int[] k = new int[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.fi();
            }
            return k;
        }

        long[] nl(int n) {
            long[] k = new long[n];
            for (int i = 0; i < n; i++) {
                k[i] = sc.nextLong();
            }
            return k;
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int fi() {
            String t = next();
            int cur = 0;
            boolean n = t.charAt(0) == '-';
            for (int a = n ? 1 : 0; a < t.length(); a++) {
                cur = cur * 10 + t.charAt(a) - '0';
            }
            return n ? -cur : cur;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }


}