0fce772883 2015-11-18        kinaba: #include <iostream>
0fce772883 2015-11-18        kinaba: #include <sstream>
0fce772883 2015-11-18        kinaba: #include <iomanip>
0fce772883 2015-11-18        kinaba: #include <vector>
0fce772883 2015-11-18        kinaba: #include <string>
0fce772883 2015-11-18        kinaba: #include <map>
0fce772883 2015-11-18        kinaba: #include <set>
0fce772883 2015-11-18        kinaba: #include <algorithm>
0fce772883 2015-11-18        kinaba: #include <numeric>
0fce772883 2015-11-18        kinaba: #include <iterator>
0fce772883 2015-11-18        kinaba: #include <functional>
0fce772883 2015-11-18        kinaba: #include <complex>
0fce772883 2015-11-18        kinaba: #include <queue>
0fce772883 2015-11-18        kinaba: #include <stack>
0fce772883 2015-11-18        kinaba: #include <cmath>
0fce772883 2015-11-18        kinaba: #include <cassert>
0fce772883 2015-11-18        kinaba: #include <tuple>
0fce772883 2015-11-18        kinaba: using namespace std;
0fce772883 2015-11-18        kinaba: typedef long long LL;
0fce772883 2015-11-18        kinaba: typedef complex<double> CMP;
0fce772883 2015-11-18        kinaba: 
0fce772883 2015-11-18        kinaba: static const unsigned MODVAL = 1000000007;
0fce772883 2015-11-18        kinaba: struct mint
0fce772883 2015-11-18        kinaba: {
0fce772883 2015-11-18        kinaba: 	unsigned val;
0fce772883 2015-11-18        kinaba: 	mint():val(0){}
0fce772883 2015-11-18        kinaba: 	mint(int      x):val(x%MODVAL) {}
0fce772883 2015-11-18        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
0fce772883 2015-11-18        kinaba: 	mint(LL       x):val(x%MODVAL) {}
0fce772883 2015-11-18        kinaba: };
0fce772883 2015-11-18        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
0fce772883 2015-11-18        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
0fce772883 2015-11-18        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
0fce772883 2015-11-18        kinaba: mint operator+(mint x, mint y) { return x+=y; }
0fce772883 2015-11-18        kinaba: mint operator-(mint x, mint y) { return x-=y; }
0fce772883 2015-11-18        kinaba: mint operator*(mint x, mint y) { return x*=y; }
0fce772883 2015-11-18        kinaba: mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
0fce772883 2015-11-18        kinaba: mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL-2); }
0fce772883 2015-11-18        kinaba: mint operator/(mint x, mint y) { return x/=y; }
0fce772883 2015-11-18        kinaba: vector<mint> FAC_(1,1);
0fce772883 2015-11-18        kinaba: mint FAC(LL n) { while( FAC_.size()<=n ) FAC_.push_back( FAC_.back()*LL(FAC_.size()) ); return FAC_[n]; }
0fce772883 2015-11-18        kinaba: 
0fce772883 2015-11-18        kinaba: // nCk :: O(1) time, O(n^2) space.
0fce772883 2015-11-18        kinaba: vector< vector<mint> > CP_;
0fce772883 2015-11-18        kinaba: mint C(int n, int k) {
0fce772883 2015-11-18        kinaba: 	while( CP_.size() <= n ) {
0fce772883 2015-11-18        kinaba: 		int nn = CP_.size();
0fce772883 2015-11-18        kinaba: 		CP_.push_back(vector<mint>(nn+1,1));
0fce772883 2015-11-18        kinaba: 		for(int kk=1; kk<nn; ++kk)
0fce772883 2015-11-18        kinaba: 			CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
0fce772883 2015-11-18        kinaba: 	}
0fce772883 2015-11-18        kinaba: 	return k<0 || n<k ? 0 : CP_[n][k];
0fce772883 2015-11-18        kinaba: }
0fce772883 2015-11-18        kinaba: 
0fce772883 2015-11-18        kinaba: class AlmostEulerianGraph { public:
0fce772883 2015-11-18        kinaba: 	int calculateGraphs(int n)
0fce772883 2015-11-18        kinaba: 	{
0fce772883 2015-11-18        kinaba: 		memo.assign(n+1, -1);
0fce772883 2015-11-18        kinaba: 		return (calcExactEulerian(n) * (LL(n)*(n-1)/2+1)).val;
0fce772883 2015-11-18        kinaba: 	}
0fce772883 2015-11-18        kinaba: 
0fce772883 2015-11-18        kinaba: 	vector<int> memo;
0fce772883 2015-11-18        kinaba: 	mint calcExactEulerian(int n)
0fce772883 2015-11-18        kinaba: 	{
0fce772883 2015-11-18        kinaba: 		if(n == 1)
0fce772883 2015-11-18        kinaba: 			return 1;
0fce772883 2015-11-18        kinaba: 		if(memo[n] != -1)
0fce772883 2015-11-18        kinaba: 			return memo[n];
0fce772883 2015-11-18        kinaba: 
0fce772883 2015-11-18        kinaba: 		mint sum = 0;
0fce772883 2015-11-18        kinaba: 		for(int k=1; k<n; ++k)
0fce772883 2015-11-18        kinaba: 			sum += k * C(n, k) * POW(2, C(n-k-1, 2).val) * calcExactEulerian(k);
0fce772883 2015-11-18        kinaba: 		return memo[n] = (POW(2, C(n-1, 2).val) - sum/n).val;
0fce772883 2015-11-18        kinaba: 	}
0fce772883 2015-11-18        kinaba: };
0fce772883 2015-11-18        kinaba: 
0fce772883 2015-11-18        kinaba: // BEGIN CUT HERE
0fce772883 2015-11-18        kinaba: #include <ctime>
0fce772883 2015-11-18        kinaba: double start_time; string timer()
0fce772883 2015-11-18        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
0fce772883 2015-11-18        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
0fce772883 2015-11-18        kinaba:  { os << "{ ";
0fce772883 2015-11-18        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
0fce772883 2015-11-18        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
0fce772883 2015-11-18        kinaba: void verify_case(const int& Expected, const int& Received) {
0fce772883 2015-11-18        kinaba:  bool ok = (Expected == Received);
0fce772883 2015-11-18        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
0fce772883 2015-11-18        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
0fce772883 2015-11-18        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
0fce772883 2015-11-18        kinaba: #define END	 verify_case(_, AlmostEulerianGraph().calculateGraphs(n));}
0fce772883 2015-11-18        kinaba: int main(){
0fce772883 2015-11-18        kinaba: 
0fce772883 2015-11-18        kinaba: CASE(0)
0fce772883 2015-11-18        kinaba: 	int n = 3;
0fce772883 2015-11-18        kinaba: 	int _ = 4;
0fce772883 2015-11-18        kinaba: END
0fce772883 2015-11-18        kinaba: CASE(1)
0fce772883 2015-11-18        kinaba: 	int n = 2;
0fce772883 2015-11-18        kinaba: 	int _ = 0;
0fce772883 2015-11-18        kinaba: END
0fce772883 2015-11-18        kinaba: CASE(2)
0fce772883 2015-11-18        kinaba: 	int n = 42;
0fce772883 2015-11-18        kinaba: 	int _ = 29010676;
0fce772883 2015-11-18        kinaba: END
0fce772883 2015-11-18        kinaba: CASE(3)
0fce772883 2015-11-18        kinaba: 	int n = 2000;
0fce772883 2015-11-18        kinaba: 	int _ = -1;
0fce772883 2015-11-18        kinaba: END
0fce772883 2015-11-18        kinaba: /*
0fce772883 2015-11-18        kinaba: CASE(4)
0fce772883 2015-11-18        kinaba: 	int n = ;
0fce772883 2015-11-18        kinaba: 	int _ = ;
0fce772883 2015-11-18        kinaba: END
0fce772883 2015-11-18        kinaba: */
0fce772883 2015-11-18        kinaba: }
0fce772883 2015-11-18        kinaba: // END CUT HERE