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 CPP):

Solution:
#include <bits/stdc++.h>
template <typename T, typename = std::true_type>
struct IdentityHelper;
template <typename T>
struct IdentityHelper<T, typename std::is_arithmetic<T>::type> {
  static T identity() { return 1; }
};
template <typename T>
T identity() {
  return IdentityHelper<T>::identity();
}
template <typename T>
T extendedGcd(T a, T b, T& x, T& y) {
  if (a == 0) {
    x = 0;
    y = 1;
    return b;
  }
  T d = extendedGcd(b % a, a, y, x);
  x -= (b / a) * y;
  return d;
}
template <typename T>
class Zn {
 public:
  Zn() : value(0) {}
  static Zn valueOf(int value) {
    int x = value % mod();
    if (x < 0) {
      x += mod();
    }
    return Zn(x);
  }
  static Zn valueOf(long long value) {
    int x = static_cast<int>(value % mod());
    if (x < 0) {
      x += mod();
    }
    return Zn(x);
  }
  static Zn rawValueOf(int value) {
    ;
    return Zn(value);
  }
  Zn& operator=(int rhs) { return *this = Zn::valueOf(rhs); }
  Zn& operator=(long long rhs) { return *this = Zn::valueOf(rhs); }
  Zn& operator+=(const Zn& rhs) {
    value += rhs.value;
    if (value >= mod()) {
      value -= mod();
    }
    return *this;
  }
  Zn& operator+=(int rhs) { return *this += Zn::valueOf(rhs); }
  Zn& operator+=(long long rhs) { return *this += Zn::valueOf(rhs); }
  Zn& operator-=(const Zn& rhs) {
    value -= rhs.value;
    if (value < 0) {
      value += mod();
    }
    return *this;
  }
  Zn& operator-=(int rhs) { return *this -= Zn::valueOf(rhs); }
  Zn& operator-=(long long rhs) { return *this -= Zn::valueOf(rhs); }
  Zn& operator*=(const Zn& rhs) {
    long long result =
        static_cast<long long>(value) * static_cast<long long>(rhs.value);
    value = static_cast<int>(result % mod());
    return *this;
  }
  Zn& operator*=(int rhs) { return *this *= Zn::valueOf(rhs); }
  Zn& operator*=(long long rhs) { return *this *= Zn::valueOf(rhs); }
  Zn operator-() const {
    if (value == 0) {
      return *this;
    } else {
      return Zn(mod() - value);
    }
  }
  Zn& operator/=(const Zn& rhs) { return *this *= rhs.inversed(); }
  Zn& operator/=(int rhs) { return *this /= Zn::valueOf(rhs); }
  Zn& operator/=(long long rhs) { return *this /= Zn::valueOf(rhs); }
  bool operator==(const Zn& rhs) const { return value == rhs.value; }
  Zn inversed() const {
    ;
    int x, y;
    int gcd = extendedGcd(value, mod(), x, y);
    (void)gcd;
    ;
    if (x < 0) {
      x += mod();
    }
    return Zn(x);
  }
  template <typename U>
  friend std::ostream& operator<<(std::ostream&, const Zn<U>& zn);
  template <typename U>
  friend std::istream& operator>>(std::istream&, Zn<U>& zn);
  int intValue() const { return value; }

 private:
  explicit Zn(int value) : value(value) {}
  int value;
  constexpr static int mod() { return T::value; }
  template <int N = T::value>
  static constexpr bool positive_or_runtime(int) {
    return N > 0;
  }
  static constexpr bool positive_or_runtime(...) { return true; }
  static_assert(
      std::is_same<typename std::decay<decltype(T::value)>::type, int>::value,
      "T::value must be int");
  static_assert(positive_or_runtime(0), "Mod has to be positive integer");
};
template <typename T>
bool operator==(const Zn<T>& lhs, int rhs) {
  return lhs == Zn<T>::valueOf(rhs);
}
template <typename T>
bool operator==(int lhs, const Zn<T>& rhs) {
  return rhs == lhs;
}
template <typename T>
bool operator==(const Zn<T>& lhs, long long rhs) {
  return lhs == Zn<T>::valueOf(rhs);
}
template <typename T>
bool operator==(long long lhs, Zn<T>& rhs) {
  return rhs == lhs;
}
template <typename T>
bool operator!=(const Zn<T>& lhs, const Zn<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator!=(const Zn<T>& lhs, int rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator!=(int lhs, const Zn<T>& rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator!=(const Zn<T>& lhs, long long rhs) {
  return !(lhs == rhs);
}
template <typename T>
bool operator!=(long long rhs, const Zn<T>& lhs) {
  return !(lhs == rhs);
}
template <typename T>
Zn<T> operator+(const Zn<T>& lhs, const Zn<T>& rhs) {
  Zn<T> copy = lhs;
  return copy += rhs;
}
template <typename T>
Zn<T> operator+(const Zn<T>& lhs, int rhs) {
  Zn<T> copy = lhs;
  return copy += rhs;
}
template <typename T>
Zn<T> operator+(int lhs, const Zn<T>& rhs) {
  return rhs + lhs;
}
template <typename T>
Zn<T> operator+(const Zn<T>& lhs, long long rhs) {
  Zn<T> copy = lhs;
  return copy += rhs;
}
template <typename T>
Zn<T> operator+(long long lhs, const Zn<T>& rhs) {
  return rhs + lhs;
}
template <typename T>
Zn<T> operator-(const Zn<T>& lhs, const Zn<T>& rhs) {
  Zn<T> copy = lhs;
  return copy -= rhs;
}
template <typename T>
Zn<T> operator-(const Zn<T>& lhs, int rhs) {
  Zn<T> copy = lhs;
  return copy -= rhs;
}
template <typename T>
Zn<T> operator-(int lhs, const Zn<T>& rhs) {
  return Zn<T>::valueOf(lhs) - rhs;
}
template <typename T>
Zn<T> operator-(const Zn<T>& lhs, long long rhs) {
  Zn<T> copy = lhs;
  return copy -= rhs;
}
template <typename T>
Zn<T> operator-(long lhs, const Zn<T>& rhs) {
  return Zn<T>::valueOf(lhs) - rhs;
}
template <typename T>
Zn<T> operator*(const Zn<T>& lhs, const Zn<T>& rhs) {
  Zn<T> copy = lhs;
  return copy *= rhs;
}
template <typename T>
Zn<T> operator*(const Zn<T>& lhs, int rhs) {
  Zn<T> copy = lhs;
  return copy *= rhs;
}
template <typename T>
Zn<T> operator*(int lhs, const Zn<T>& rhs) {
  return rhs * lhs;
}
template <typename T>
Zn<T> operator*(const Zn<T>& lhs, long long rhs) {
  Zn<T> copy = lhs;
  return copy *= rhs;
}
template <typename T>
Zn<T> operator*(long long lhs, const Zn<T>& rhs) {
  return rhs * lhs;
}
template <typename T>
Zn<T> operator/(const Zn<T>& lhs, const Zn<T>& rhs) {
  Zn<T> copy = lhs;
  return copy /= rhs;
}
template <typename T>
Zn<T> operator/(const Zn<T>& lhs, int rhs) {
  Zn<T> copy = lhs;
  return copy /= rhs;
}
template <typename T>
Zn<T> operator/(int lhs, const Zn<T>& rhs) {
  return Zn<T>::valueOf(lhs) / rhs;
}
template <typename T>
Zn<T> operator/(const Zn<T>& lhs, long long rhs) {
  Zn<T> copy = lhs;
  return copy /= rhs;
}
template <typename T>
Zn<T> operator/(long long lhs, const Zn<T>& rhs) {
  return Zn<T>::valueOf(lhs) / rhs;
}
template <typename T>
std::ostream& operator<<(std::ostream& stream, const Zn<T>& zn) {
  return stream << zn.value;
}
template <typename T>
std::istream& operator>>(std::istream& stream, Zn<T>& zn) {
  long long value;
  stream >> value;
  zn.value = static_cast<int>(value % T::value);
  return stream;
}
template <typename T>
struct IdentityHelper<Zn<T>> {
  static Zn<T> identity() { return Zn<T>::valueOf(1); }
};
template <int m>
using ZnConst = Zn<std::integral_constant<int, m>>;
template <typename T>
class IntegerIterator
    : public std::iterator<std::input_iterator_tag, T, std::ptrdiff_t, T*, T> {
 public:
  explicit IntegerIterator(T value) : value(value) {}
  IntegerIterator& operator++() {
    ++value;
    return *this;
  }
  IntegerIterator operator++(int) {
    IntegerIterator copy = *this;
    ++value;
    return copy;
  }
  IntegerIterator& operator--() {
    --value;
    return *this;
  }
  IntegerIterator operator--(int) {
    IntegerIterator copy = *this;
    --value;
    return copy;
  }
  T operator*() const { return value; }
  bool operator==(IntegerIterator rhs) const { return value == rhs.value; }
  bool operator!=(IntegerIterator rhs) const { return !(*this == rhs); }

 private:
  T value;
};
template <typename T>
class IntegerRange {
 public:
  IntegerRange(T begin, T end) : begin_(begin), end_(end) { ; }
  IntegerIterator<T> begin() const { return IntegerIterator<T>(begin_); }
  IntegerIterator<T> end() const { return IntegerIterator<T>(end_); }

 private:
  T begin_;
  T end_;
};
template <typename T>
class ReversedIntegerRange {
 public:
  ReversedIntegerRange(T begin, T end) : begin_(begin), end_(end) { ; }
  std::reverse_iterator<IntegerIterator<T>> begin() const {
    return std::reverse_iterator<IntegerIterator<T>>(
        IntegerIterator<T>(begin_));
  }
  std::reverse_iterator<IntegerIterator<T>> end() const {
    return std::reverse_iterator<IntegerIterator<T>>(IntegerIterator<T>(end_));
  }

 private:
  T begin_;
  T end_;
};
template <typename T>
IntegerRange<T> range(T to) {
  return IntegerRange<T>(0, to);
}
template <typename T>
IntegerRange<T> range(T from, T to) {
  return IntegerRange<T>(from, to);
}
template <typename T>
IntegerRange<T> inclusiveRange(T to) {
  return IntegerRange<T>(0, to + 1);
}
template <typename T>
IntegerRange<T> inclusiveRange(T from, T to) {
  return IntegerRange<T>(from, to + 1);
}
template <typename T>
ReversedIntegerRange<T> downrange(T from) {
  return ReversedIntegerRange<T>(from, 0);
}
template <typename T>
ReversedIntegerRange<T> downrange(T from, T to) {
  return ReversedIntegerRange<T>(from, to);
}
template <typename T>
ReversedIntegerRange<T> inclusiveDownrange(T from) {
  return ReversedIntegerRange<T>(from + 1, 0);
}
template <typename T>
ReversedIntegerRange<T> inclusiveDownrange(T from, T to) {
  return ReversedIntegerRange<T>(from + 1, to);
}
using namespace std;
class TaskC {
 public:
  using Z = ZnConst<1000000007>;
  vector<vector<int>> g;
  using T = std::array<std::array<Z, 3>, 11>;
  int k, x;
  T dfs(int v, int p) {
    T res;
    res[0][0] = k;
    res[1][1] = 1;
    res[0][2] = m - k - 1;
    for (int to : g[v]) {
      if (to == p) {
        continue;
      }
      T newRes;
      auto other = dfs(to, v);
      for (int i : range(11)) {
        for (int j : range(11 - i)) {
          newRes[i + j][0] +=
              res[i][0] * (other[j][0] + other[j][1] + other[j][2]);
          newRes[i + j][1] += res[i][1] * (other[j][0]);
          newRes[i + j][2] += res[i][2] * (other[j][0] + other[j][2]);
        }
      }
      res = newRes;
    }
    return res;
  }
  int m;
  void solve(std::istream& in, std::ostream& out) {
    int n;
    in >> n >> m;
    g.resize(n);
    for (int i : range(n - 1)) {
      int a, b;
      in >> a >> b;
      --a, --b;
      g[a].push_back(b);
      g[b].push_back(a);
    }
    in >> k >> x;
    --k;
    auto res = dfs(0, 0);
    Z ans;
    for (int i : range(x + 1)) {
      for (int j : range(3)) {
        ans += res[i][j];
      }
    }
    out << ans << "\n";
  }
};
int main() {
  std::ios_base::sync_with_stdio(false);
  TaskC solver;
  std::istream& in(std::cin);
  std::ostream& out(std::cout);
  in.tie(nullptr);
  out << std::fixed;
  out.precision(20);
  solver.solve(in, out);
  return 0;
}