ddf2358d33 2012-08-08        kinaba: #include <iostream>
ddf2358d33 2012-08-08        kinaba: #include <sstream>
ddf2358d33 2012-08-08        kinaba: #include <iomanip>
ddf2358d33 2012-08-08        kinaba: #include <vector>
ddf2358d33 2012-08-08        kinaba: #include <string>
ddf2358d33 2012-08-08        kinaba: #include <map>
ddf2358d33 2012-08-08        kinaba: #include <set>
ddf2358d33 2012-08-08        kinaba: #include <algorithm>
ddf2358d33 2012-08-08        kinaba: #include <numeric>
ddf2358d33 2012-08-08        kinaba: #include <iterator>
ddf2358d33 2012-08-08        kinaba: #include <functional>
ddf2358d33 2012-08-08        kinaba: #include <complex>
ddf2358d33 2012-08-08        kinaba: #include <queue>
ddf2358d33 2012-08-08        kinaba: #include <stack>
ddf2358d33 2012-08-08        kinaba: #include <cmath>
ddf2358d33 2012-08-08        kinaba: #include <cassert>
ddf2358d33 2012-08-08        kinaba: using namespace std;
ddf2358d33 2012-08-08        kinaba: typedef long long LL;
ddf2358d33 2012-08-08        kinaba: typedef long double LD;
ddf2358d33 2012-08-08        kinaba: typedef complex<LD> CMP;
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: static const int MODVAL = 1000000007;
ddf2358d33 2012-08-08        kinaba: struct mint
ddf2358d33 2012-08-08        kinaba: {
ddf2358d33 2012-08-08        kinaba: 	int val;
ddf2358d33 2012-08-08        kinaba: 	mint():val(0){}
ddf2358d33 2012-08-08        kinaba: 	mint(int    x):val(x%MODVAL) {}
ddf2358d33 2012-08-08        kinaba: 	mint(size_t x):val(x%MODVAL) {}
ddf2358d33 2012-08-08        kinaba: 	mint(LL     x):val(x%MODVAL) {}
ddf2358d33 2012-08-08        kinaba: };
ddf2358d33 2012-08-08        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
ddf2358d33 2012-08-08        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
ddf2358d33 2012-08-08        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
ddf2358d33 2012-08-08        kinaba: mint operator+(mint x, mint y) { return x+=y; }
ddf2358d33 2012-08-08        kinaba: mint operator-(mint x, mint y) { return x-=y; }
ddf2358d33 2012-08-08        kinaba: mint operator*(mint x, mint y) { return x*=y; }
ddf2358d33 2012-08-08        kinaba: vector< vector<mint> > CP_;
ddf2358d33 2012-08-08        kinaba: mint C(LL n, LL k) {
ddf2358d33 2012-08-08        kinaba: 	while( CP_.size() <= n ) {
ddf2358d33 2012-08-08        kinaba: 		int nn = CP_.size();
ddf2358d33 2012-08-08        kinaba: 		CP_.push_back(vector<mint>(nn+1,1));
ddf2358d33 2012-08-08        kinaba: 		for(int kk=1; kk<nn; ++kk)
ddf2358d33 2012-08-08        kinaba: 			CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
ddf2358d33 2012-08-08        kinaba: 	}
ddf2358d33 2012-08-08        kinaba: 	return k<0 || n<k ? 0 : CP_[n][k];
ddf2358d33 2012-08-08        kinaba: }
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: class KingdomAndCities { public:
ddf2358d33 2012-08-08        kinaba: 	int howMany(int N, int M, int K)
ddf2358d33 2012-08-08        kinaba: 	{
ddf2358d33 2012-08-08        kinaba: 		if( M == 0 ) return zero(N, K).val;
ddf2358d33 2012-08-08        kinaba: 		if( M == 1 ) return one(N, K).val;
ddf2358d33 2012-08-08        kinaba: 		return two(N, K).val;
ddf2358d33 2012-08-08        kinaba: 	}
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: 	mint zero_may_be_disconnected(int N, int K)
ddf2358d33 2012-08-08        kinaba: 	{
ddf2358d33 2012-08-08        kinaba: 		return C(N*(N-1)/2, K);
ddf2358d33 2012-08-08        kinaba: 	}
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: 	map<pair<int,int>, mint> memo;
ddf2358d33 2012-08-08        kinaba: 	mint zero(int N, int K)
ddf2358d33 2012-08-08        kinaba: 	{
ddf2358d33 2012-08-08        kinaba: 		pair<int,int> key(N, K);
ddf2358d33 2012-08-08        kinaba: 		if(memo.count(key))
ddf2358d33 2012-08-08        kinaba: 			return memo[key];
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: 		mint sum = zero_may_be_disconnected(N, K);
ddf2358d33 2012-08-08        kinaba: 		for(int NA=1; NA<=N-1; ++NA)
ddf2358d33 2012-08-08        kinaba: 		for(int KA=0; KA<=K; ++KA)
ddf2358d33 2012-08-08        kinaba: 			sum -= C(N-1,NA-1)*zero(NA,KA)*zero_may_be_disconnected(N-NA, K-KA);
ddf2358d33 2012-08-08        kinaba: 		return memo[key] = sum;
ddf2358d33 2012-08-08        kinaba: 	}
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: 	mint one(int N, int K)
ddf2358d33 2012-08-08        kinaba: 	{
ddf2358d33 2012-08-08        kinaba: 		mint sum = zero(N-1,K-2)*C(N-1,2);
ddf2358d33 2012-08-08        kinaba: 		for(int NA=1; NA<=N-2; ++NA)
ddf2358d33 2012-08-08        kinaba: 		for(int KA=0; KA<=K-2; ++KA)
ddf2358d33 2012-08-08        kinaba: 			sum += C(N-2,NA-1)*zero(NA,KA)*NA*(N-1-NA)*zero(N-1-NA,K-2-KA);
ddf2358d33 2012-08-08        kinaba: 		return sum;
ddf2358d33 2012-08-08        kinaba: 	}
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: 	mint two(int N, int K)
ddf2358d33 2012-08-08        kinaba: 	{
ddf2358d33 2012-08-08        kinaba: 		mint sum = one(N-1,K-2)*C(N-2,2);
ddf2358d33 2012-08-08        kinaba: 		for(int NA=1; NA<=N-2; ++NA)
ddf2358d33 2012-08-08        kinaba: 		for(int KA=0; KA<=K-2; ++KA)
ddf2358d33 2012-08-08        kinaba: 			sum += C(N-2,NA-1)*one(NA,KA)*(NA-1)*(N-1-NA)*zero(N-1-NA,K-2-KA);
ddf2358d33 2012-08-08        kinaba: 		--N, --K;
ddf2358d33 2012-08-08        kinaba: 		sum += zero(N-1,K-2)*(N-1)*(N-1);
ddf2358d33 2012-08-08        kinaba: 		for(int NA=1; NA<=N-2; ++NA)
ddf2358d33 2012-08-08        kinaba: 		for(int KA=0; KA<=K-2; ++KA)
ddf2358d33 2012-08-08        kinaba: 			sum += C(N-1,NA)*zero(NA,KA)*NA*(N-1-NA)*zero(N-1-NA,K-2-KA);
ddf2358d33 2012-08-08        kinaba: 		return sum;
ddf2358d33 2012-08-08        kinaba: 	}
ddf2358d33 2012-08-08        kinaba: };
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: // BEGIN CUT HERE
ddf2358d33 2012-08-08        kinaba: #include <ctime>
ddf2358d33 2012-08-08        kinaba: double start_time; string timer()
ddf2358d33 2012-08-08        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
ddf2358d33 2012-08-08        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
ddf2358d33 2012-08-08        kinaba:  { os << "{ ";
ddf2358d33 2012-08-08        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
ddf2358d33 2012-08-08        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
ddf2358d33 2012-08-08        kinaba: void verify_case(const int& Expected, const int& Received) {
ddf2358d33 2012-08-08        kinaba:  bool ok = (Expected == Received);
ddf2358d33 2012-08-08        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
ddf2358d33 2012-08-08        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
ddf2358d33 2012-08-08        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
ddf2358d33 2012-08-08        kinaba: #define END	 verify_case(_, KingdomAndCities().howMany(N, M, K));}
ddf2358d33 2012-08-08        kinaba: int main(){
ddf2358d33 2012-08-08        kinaba: 
ddf2358d33 2012-08-08        kinaba: CASE(0)
ddf2358d33 2012-08-08        kinaba: 	int N = 3;
ddf2358d33 2012-08-08        kinaba: 	int M = 0;
ddf2358d33 2012-08-08        kinaba: 	int K = 3;
ddf2358d33 2012-08-08        kinaba: 	int _ = 1;
ddf2358d33 2012-08-08        kinaba: END
ddf2358d33 2012-08-08        kinaba: CASE(1)
ddf2358d33 2012-08-08        kinaba: 	int N = 4;
ddf2358d33 2012-08-08        kinaba: 	int M = 1;
ddf2358d33 2012-08-08        kinaba: 	int K = 4;
ddf2358d33 2012-08-08        kinaba: 	int _ = 9;
ddf2358d33 2012-08-08        kinaba: END
ddf2358d33 2012-08-08        kinaba: CASE(2)
ddf2358d33 2012-08-08        kinaba: 	int N = 5;
ddf2358d33 2012-08-08        kinaba: 	int M = 2;
ddf2358d33 2012-08-08        kinaba: 	int K = 11;
ddf2358d33 2012-08-08        kinaba: 	int _ = 0;
ddf2358d33 2012-08-08        kinaba: END
ddf2358d33 2012-08-08        kinaba: CASE(3)
ddf2358d33 2012-08-08        kinaba: 	int N = 5;
ddf2358d33 2012-08-08        kinaba: 	int M = 0;
ddf2358d33 2012-08-08        kinaba: 	int K = 8;
ddf2358d33 2012-08-08        kinaba: 	int _ = 45;
ddf2358d33 2012-08-08        kinaba: END
ddf2358d33 2012-08-08        kinaba: CASE(4)
ddf2358d33 2012-08-08        kinaba: 	int N = 10;
ddf2358d33 2012-08-08        kinaba: 	int M = 2;
ddf2358d33 2012-08-08        kinaba: 	int K = 20;
ddf2358d33 2012-08-08        kinaba: 	int _ = 150810825;
ddf2358d33 2012-08-08        kinaba: END
ddf2358d33 2012-08-08        kinaba: CASE(5)
ddf2358d33 2012-08-08        kinaba: 	int N = 3;
ddf2358d33 2012-08-08        kinaba: 	int M = 2;
ddf2358d33 2012-08-08        kinaba: 	int K = 3;
ddf2358d33 2012-08-08        kinaba: 	int _ = 1;
ddf2358d33 2012-08-08        kinaba: END
ddf2358d33 2012-08-08        kinaba: /*
ddf2358d33 2012-08-08        kinaba: CASE(6)
ddf2358d33 2012-08-08        kinaba: 	int N = ;
ddf2358d33 2012-08-08        kinaba: 	int M = ;
ddf2358d33 2012-08-08        kinaba: 	int K = ;
ddf2358d33 2012-08-08        kinaba: 	int _ = ;
ddf2358d33 2012-08-08        kinaba: END
ddf2358d33 2012-08-08        kinaba: */
ddf2358d33 2012-08-08        kinaba: }
ddf2358d33 2012-08-08        kinaba: // END CUT HERE