#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;

namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}

  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }

  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }

  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };

  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }

  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed

  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());

  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); }

  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;


// nCk mod p, O(1)
// precomputation O(size)
class combination_mod{
  const long long mod;
  const long long size;
public:
  vector<long long> fact; //n!
  vector<long long> fact_inv; // (n!)^-1

  void make_fact(){
    fact[0] = 1;
    for(long long i=1; i<size; i++){
      fact[i] = fact[i-1]*i % mod;
    }
  }

  void make_fact_inv(){
    fact_inv[0] = fact_inv[1] = 1;
    for(long long i=2; i<size; i++){
      fact_inv[i] = fact_inv[mod%i] * (mod - mod/i) % mod;  // x ^ -1
    }
    for(int i=2; i<size; i++){
      fact_inv[i] = fact_inv[i-1] * fact_inv[i] % mod;  // x! ^ -1
    }
  }

  combination_mod(long long mod_, long long size_ = 2000000) : mod(mod_), size(size_+1){
    fact.resize(size);
    fact_inv.resize(size);
    make_fact();
    make_fact_inv();
  }

  //nCk mod p O(1)
  long long operator()(long long n, long long k){
    if(k==0 || n==k) return 1;
    long long ret = fact[n] * fact_inv[k] % mod * fact_inv[n-k] % mod;
    return ret;
  }
};

combination_mod c(mod, 200000);

void rec(vector<vector<int>>& g, int k, int pos, int par, long long& ans){
  int num_ch = g[pos].size();
  if(par != -1) num_ch--;
  int r = par == -1 ? k - 1 : k - 2;

  // paint children
  ans = ans * c(r, num_ch) % mod * c.fact[num_ch] % mod;

  for(auto v: g[pos]){
    if(v == par) continue;
    rec(g, k, v, pos, ans);
  }
}

int main(){
  int n,k;
  cin >> n,k;

  vector<vector<int>> g(n);
  for(int i=0; i<n-1; i++){
    int a,b;
    cin >> a,b;
    a--; b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }

  for(int i=0; i<n; i++){
    if(g[i].size() >= k){
      println(0);
      return 0;
    }
  }

  long long ans = k;
  rec(g, k, 0, -1, ans);
  println(ans);

  return 0;
}


Measured memory_bytes: 14720