155c399d58 2012-12-08        kinaba: #include <iostream>
155c399d58 2012-12-08        kinaba: #include <sstream>
155c399d58 2012-12-08        kinaba: #include <iomanip>
155c399d58 2012-12-08        kinaba: #include <vector>
155c399d58 2012-12-08        kinaba: #include <string>
155c399d58 2012-12-08        kinaba: #include <map>
155c399d58 2012-12-08        kinaba: #include <set>
155c399d58 2012-12-08        kinaba: #include <algorithm>
155c399d58 2012-12-08        kinaba: #include <numeric>
155c399d58 2012-12-08        kinaba: #include <iterator>
155c399d58 2012-12-08        kinaba: #include <functional>
155c399d58 2012-12-08        kinaba: #include <complex>
155c399d58 2012-12-08        kinaba: #include <queue>
155c399d58 2012-12-08        kinaba: #include <stack>
155c399d58 2012-12-08        kinaba: #include <cmath>
155c399d58 2012-12-08        kinaba: #include <cassert>
155c399d58 2012-12-08        kinaba: using namespace std;
155c399d58 2012-12-08        kinaba: typedef long long LL;
155c399d58 2012-12-08        kinaba: typedef long double LD;
155c399d58 2012-12-08        kinaba: typedef complex<LD> CMP;
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: static const unsigned MODVAL = 1000000009;
155c399d58 2012-12-08        kinaba: struct mint
155c399d58 2012-12-08        kinaba: {
155c399d58 2012-12-08        kinaba: 	unsigned val;
155c399d58 2012-12-08        kinaba: 	mint():val(0){}
155c399d58 2012-12-08        kinaba: 	mint(int      x):val(x%MODVAL) {}
155c399d58 2012-12-08        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
155c399d58 2012-12-08        kinaba: 	mint(LL       x):val(x%MODVAL) {}
155c399d58 2012-12-08        kinaba: };
155c399d58 2012-12-08        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
155c399d58 2012-12-08        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
155c399d58 2012-12-08        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
155c399d58 2012-12-08        kinaba: mint operator+(mint x, mint y) { return x+=y; }
155c399d58 2012-12-08        kinaba: mint operator-(mint x, mint y) { return x-=y; }
155c399d58 2012-12-08        kinaba: mint operator*(mint x, mint y) { return x*=y; }
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: vector<mint> FAC_(1,1);
155c399d58 2012-12-08        kinaba: mint FAC(LL n) { while( FAC_.size()<=n ) FAC_.push_back( FAC_.back()*FAC_.size() ); return FAC_[n]; }
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: // nCk :: O(1) time, O(n^2) space.
155c399d58 2012-12-08        kinaba: vector< vector<mint> > CP_;
155c399d58 2012-12-08        kinaba: mint C(LL n, LL k) {
155c399d58 2012-12-08        kinaba: 	while( CP_.size() <= n ) {
155c399d58 2012-12-08        kinaba: 		int nn = CP_.size();
155c399d58 2012-12-08        kinaba: 		CP_.push_back(vector<mint>(nn+1,1));
155c399d58 2012-12-08        kinaba: 		for(int kk=1; kk<nn; ++kk)
155c399d58 2012-12-08        kinaba: 			CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
155c399d58 2012-12-08        kinaba: 	}
155c399d58 2012-12-08        kinaba: 	return k<0 || n<k ? 0 : CP_[n][k];
155c399d58 2012-12-08        kinaba: }
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: class InducedSubgraphs { public:
155c399d58 2012-12-08        kinaba: 	int getCount(vector <int> edge1, vector <int> edge2, int k)
155c399d58 2012-12-08        kinaba: 	{
155c399d58 2012-12-08        kinaba: 		int N = edge1.size()+1;
155c399d58 2012-12-08        kinaba: 		vector< vector<int> > G(N);
155c399d58 2012-12-08        kinaba: 		for(int i=0; i<edge1.size(); ++i)
155c399d58 2012-12-08        kinaba: 		{
155c399d58 2012-12-08        kinaba: 			int v = edge1[i], u = edge2[i];
155c399d58 2012-12-08        kinaba: 			G[v].push_back(u);
155c399d58 2012-12-08        kinaba: 			G[u].push_back(v);
155c399d58 2012-12-08        kinaba: 		}
155c399d58 2012-12-08        kinaba: 		return solve(G, N, k).val;
155c399d58 2012-12-08        kinaba: 	}
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 	mint solve(const vector<vector<int> >& G, int N, int K)
155c399d58 2012-12-08        kinaba: 	{
155c399d58 2012-12-08        kinaba: 		mint total = 0;
155c399d58 2012-12-08        kinaba: 		for(int root=0; root<N; ++root)
155c399d58 2012-12-08        kinaba: 			total += solve_rooted(G, N, K, root);
155c399d58 2012-12-08        kinaba: 		return total;
155c399d58 2012-12-08        kinaba: 	}
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 	mint solve_rooted(const vector<vector<int> >& G, int N, int K, int root)
155c399d58 2012-12-08        kinaba: 	{
155c399d58 2012-12-08        kinaba: 		memo.clear();
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 		int pre = -1, cur = root;
155c399d58 2012-12-08        kinaba: 		for(int below=N,above=0 ;; --below,++above)
155c399d58 2012-12-08        kinaba: 			if(below <= K) {
155c399d58 2012-12-08        kinaba: 				mint b = rec(G, pre, cur).second;
155c399d58 2012-12-08        kinaba: 				mint a = (above>=K-1 ? mint(1) : FAC(K-above));
155c399d58 2012-12-08        kinaba: 				return b*a;
155c399d58 2012-12-08        kinaba: 			} else {
155c399d58 2012-12-08        kinaba: 				if((pre==-1 && G[cur].size()>=2) || G[cur].size()>=3) {
155c399d58 2012-12-08        kinaba: 					// fill_branch
155c399d58 2012-12-08        kinaba: /*
155c399d58 2012-12-08        kinaba: 					vector< pair<int,int> > v_sz;
155c399d58 2012-12-08        kinaba: 					for(int k=0; k<G[cur].size(); ++k) if(G[cur][k] != pre)
155c399d58 2012-12-08        kinaba: 						v_sz.push_back(make_pair(G[cur][k], rec(G, cur, G[cur][k])));
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 					int total_size = 0;
155c399d58 2012-12-08        kinaba: 					for(int k=0; k<v_sz.size(); ++k)
155c399d58 2012-12-08        kinaba: 						total_size += v_sz[k].second;
155c399d58 2012-12-08        kinaba: 					for(int k=0; k<v_sz.size(); ++k)
155c399d58 2012-12-08        kinaba: 						if( v_sz[k].second+1 <= K )
155c399d58 2012-12-08        kinaba: */
155c399d58 2012-12-08        kinaba: 					return 0;
155c399d58 2012-12-08        kinaba: 				}
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 				int nex = (G[cur][0]!=pre ? G[cur][0] : G[cur][1]);
155c399d58 2012-12-08        kinaba: 				pre = cur;
155c399d58 2012-12-08        kinaba: 				cur = nex;
155c399d58 2012-12-08        kinaba: 			}
155c399d58 2012-12-08        kinaba: 	}
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 	// (size, number of toplofical sorting).
155c399d58 2012-12-08        kinaba: 	map<int, pair<int,mint> > memo;
155c399d58 2012-12-08        kinaba: 	pair<int,mint> rec(const vector<vector<int> >& G, int pre, int cur)
155c399d58 2012-12-08        kinaba: 	{
155c399d58 2012-12-08        kinaba: 		if(memo.count(cur))
155c399d58 2012-12-08        kinaba: 			return memo[cur];
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 		vector< pair<int,mint> > children;
155c399d58 2012-12-08        kinaba: 		for(int i=0; i<G[cur].size(); ++i) if(G[cur][i] != pre)
155c399d58 2012-12-08        kinaba: 			children.push_back(rec(G, cur, G[cur][i]));
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: 		mint pat  = 1;
155c399d58 2012-12-08        kinaba: 		int  size = 0;
155c399d58 2012-12-08        kinaba: 		for(int i=0; i<children.size(); ++i) {
155c399d58 2012-12-08        kinaba: 			size += children[i].first;
155c399d58 2012-12-08        kinaba: 			pat   = pat * C(size, children[i].first) * children[i].second;
155c399d58 2012-12-08        kinaba: 		}
155c399d58 2012-12-08        kinaba: 		return memo[cur] = make_pair(size+1, pat);
155c399d58 2012-12-08        kinaba: 	}
155c399d58 2012-12-08        kinaba: };
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: // BEGIN CUT HERE
155c399d58 2012-12-08        kinaba: #include <ctime>
155c399d58 2012-12-08        kinaba: double start_time; string timer()
155c399d58 2012-12-08        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
155c399d58 2012-12-08        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
155c399d58 2012-12-08        kinaba:  { os << "{ ";
155c399d58 2012-12-08        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
155c399d58 2012-12-08        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
155c399d58 2012-12-08        kinaba: void verify_case(const int& Expected, const int& Received) {
155c399d58 2012-12-08        kinaba:  bool ok = (Expected == Received);
155c399d58 2012-12-08        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
155c399d58 2012-12-08        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
155c399d58 2012-12-08        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
155c399d58 2012-12-08        kinaba: #define END	 verify_case(_, InducedSubgraphs().getCount(edge1, edge2, k));}
155c399d58 2012-12-08        kinaba: int main(){
155c399d58 2012-12-08        kinaba: 
155c399d58 2012-12-08        kinaba: CASE(0)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = {0, 1};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = {1, 2};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = 2;
155c399d58 2012-12-08        kinaba: 	int _ = 2;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: CASE(1)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = {0, 1, 3};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = {2, 2, 2};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = 3;
155c399d58 2012-12-08        kinaba: 	int _ = 12;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: CASE(2)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = {5, 0, 1, 2, 2};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = {0, 1, 2, 4, 3};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = 3;
155c399d58 2012-12-08        kinaba: 	int _ = 4;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: CASE(3)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = {0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = 11;
155c399d58 2012-12-08        kinaba: 	int _ = 481904640;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: CASE(4)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = {5, 9, 4, 10, 10, 0, 7, 6, 2, 1, 11, 8}
155c399d58 2012-12-08        kinaba: ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = {0, 0, 10, 3, 0, 6, 1, 1, 12, 12, 7, 11}
155c399d58 2012-12-08        kinaba: ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = 6;
155c399d58 2012-12-08        kinaba: 	int _ = 800;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: CASE(5)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = {0, 5, 1, 0, 2, 3, 5}
155c399d58 2012-12-08        kinaba: ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = {4, 7, 0, 6, 7, 5, 0}
155c399d58 2012-12-08        kinaba: ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = 3;
155c399d58 2012-12-08        kinaba: 	int _ = 0;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: CASE(6)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20};
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = 1;
155c399d58 2012-12-08        kinaba: 	int _ = 890964601;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: /*
155c399d58 2012-12-08        kinaba: CASE(7)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = ;
155c399d58 2012-12-08        kinaba: 	int _ = ;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: CASE(8)
155c399d58 2012-12-08        kinaba: 	int edge1_[] = ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge1(edge1_, edge1_+sizeof(edge1_)/sizeof(*edge1_));
155c399d58 2012-12-08        kinaba: 	int edge2_[] = ;
155c399d58 2012-12-08        kinaba: 	  vector <int> edge2(edge2_, edge2_+sizeof(edge2_)/sizeof(*edge2_));
155c399d58 2012-12-08        kinaba: 	int k = ;
155c399d58 2012-12-08        kinaba: 	int _ = ;
155c399d58 2012-12-08        kinaba: END
155c399d58 2012-12-08        kinaba: */
155c399d58 2012-12-08        kinaba: }
155c399d58 2012-12-08        kinaba: // END CUT HERE