4fd800b3a8 2011-02-23        kinaba: #include <iostream>
4fd800b3a8 2011-02-23        kinaba: #include <sstream>
4fd800b3a8 2011-02-23        kinaba: #include <iomanip>
4fd800b3a8 2011-02-23        kinaba: #include <vector>
4fd800b3a8 2011-02-23        kinaba: #include <string>
4fd800b3a8 2011-02-23        kinaba: #include <map>
4fd800b3a8 2011-02-23        kinaba: #include <set>
4fd800b3a8 2011-02-23        kinaba: #include <algorithm>
4fd800b3a8 2011-02-23        kinaba: #include <numeric>
4fd800b3a8 2011-02-23        kinaba: #include <iterator>
4fd800b3a8 2011-02-23        kinaba: #include <functional>
4fd800b3a8 2011-02-23        kinaba: #include <complex>
4fd800b3a8 2011-02-23        kinaba: #include <queue>
4fd800b3a8 2011-02-23        kinaba: #include <stack>
4fd800b3a8 2011-02-23        kinaba: #include <cmath>
4fd800b3a8 2011-02-23        kinaba: #include <cassert>
4fd800b3a8 2011-02-23        kinaba: #include <cstring>
4fd800b3a8 2011-02-23        kinaba: using namespace std;
4fd800b3a8 2011-02-23        kinaba: typedef long long LL;
4fd800b3a8 2011-02-23        kinaba: typedef complex<double> CMP;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: static const int MODVAL = 1000000007;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: bool is_square_free(int n)
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: 	for(int p=2; p*p<=n; ++p)
4fd800b3a8 2011-02-23        kinaba: 		if( n%(p*p) == 0 )
4fd800b3a8 2011-02-23        kinaba: 			return false;
4fd800b3a8 2011-02-23        kinaba: 	return true;
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: static const int SP[] = {2,3,5,7,11,13,17,19}; // <= sqrt(N)
4fd800b3a8 2011-02-23        kinaba: static const int SPN  = sizeof(SP)/sizeof(*SP);
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: int small_prime_mask(int n)
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: 	int m = 0;
4fd800b3a8 2011-02-23        kinaba: 	for(int i=0; i<SPN; ++i)
4fd800b3a8 2011-02-23        kinaba: 		if( n%SP[i] == 0 )
4fd800b3a8 2011-02-23        kinaba: 			m |= 1<<i;
4fd800b3a8 2011-02-23        kinaba: 	return m;
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: int big_prime_factor(int n)
4fd800b3a8 2011-02-23        kinaba: {
4fd800b3a8 2011-02-23        kinaba: 	for(int i=0; i<SPN; ++i)
4fd800b3a8 2011-02-23        kinaba: 		while( n%SP[i] == 0 )
4fd800b3a8 2011-02-23        kinaba: 			n /= SP[i];
4fd800b3a8 2011-02-23        kinaba: 	return n;
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class SquareFreeSets {
4fd800b3a8 2011-02-23        kinaba: public:
4fd800b3a8 2011-02-23        kinaba: 	int countPerfect(int N, int K)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		// way[k][m] = # of ways to make a k-elem psf-set with small prime factors m
4fd800b3a8 2011-02-23        kinaba: 		int way[501][1<<SPN] = {};
4fd800b3a8 2011-02-23        kinaba: 		way[0][0] = 1;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		for(int n=2; n<=N; ++n)
4fd800b3a8 2011-02-23        kinaba: 			if( is_square_free(n) )
4fd800b3a8 2011-02-23        kinaba: 				if( big_prime_factor(n) == 1 )
4fd800b3a8 2011-02-23        kinaba: 				{
4fd800b3a8 2011-02-23        kinaba: 					int mask = small_prime_mask(n);
4fd800b3a8 2011-02-23        kinaba: 					for(int k=K; k>=1; --k)
4fd800b3a8 2011-02-23        kinaba: 						for(int m=0; m<(1<<SPN); ++m)
4fd800b3a8 2011-02-23        kinaba: 							if( (m|mask) == m )
4fd800b3a8 2011-02-23        kinaba: 								way[k][m] = (way[k][m] + way[k-1][m&~mask]) % MODVAL;
4fd800b3a8 2011-02-23        kinaba: 				}
4fd800b3a8 2011-02-23        kinaba: 				else if( big_prime_factor(n) == n )
4fd800b3a8 2011-02-23        kinaba: 				{
4fd800b3a8 2011-02-23        kinaba: 					vector<int> mask;
4fd800b3a8 2011-02-23        kinaba: 					for(int p=1; n*p<=N; ++p)
4fd800b3a8 2011-02-23        kinaba: 						if( is_square_free(p) )
4fd800b3a8 2011-02-23        kinaba: 							mask.push_back( small_prime_mask(p) );
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 					for(int k=K; k>=1; --k)
4fd800b3a8 2011-02-23        kinaba: 						for(int m=0; m<(1<<SPN); ++m)
4fd800b3a8 2011-02-23        kinaba: 							for(int j=0; j<mask.size(); ++j)
4fd800b3a8 2011-02-23        kinaba: 								if( (m|mask[j]) == m )
4fd800b3a8 2011-02-23        kinaba: 									way[k][m] = (way[k][m] + way[k-1][m&~mask[j]]) % MODVAL;
4fd800b3a8 2011-02-23        kinaba: 				}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		// summing up
4fd800b3a8 2011-02-23        kinaba: 		int sum = 0;
4fd800b3a8 2011-02-23        kinaba: 		for(int k=1; k<=K; ++k)
4fd800b3a8 2011-02-23        kinaba: 			for(int m=0; m<(1<<SPN); ++m)
4fd800b3a8 2011-02-23        kinaba: 				sum = (sum + way[k][m]) % MODVAL;
4fd800b3a8 2011-02-23        kinaba: 		return sum;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: };
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: // BEGIN CUT HERE
4fd800b3a8 2011-02-23        kinaba: #include <ctime>
4fd800b3a8 2011-02-23        kinaba: double start_time;string timer() { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template <typename T> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: int verify_case(const int &Expected, const int &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } return 0;}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> struct Case_ { Case_(){start_time=clock();} };
4fd800b3a8 2011-02-23        kinaba: char Test_(...);
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<0>) {
4fd800b3a8 2011-02-23        kinaba: 	int N = 5;
4fd800b3a8 2011-02-23        kinaba: 	int K = 1;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal = 3;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, SquareFreeSets().countPerfect(N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<1>) {
4fd800b3a8 2011-02-23        kinaba: 	int N = 5;
4fd800b3a8 2011-02-23        kinaba: 	int K = 2;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal = 6;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, SquareFreeSets().countPerfect(N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<2>) {
4fd800b3a8 2011-02-23        kinaba: 	int N = 5;
4fd800b3a8 2011-02-23        kinaba: 	int K = 3;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal = 7;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, SquareFreeSets().countPerfect(N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<3>) {
4fd800b3a8 2011-02-23        kinaba: 	int N = 6;
4fd800b3a8 2011-02-23        kinaba: 	int K = 3;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal = 9;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, SquareFreeSets().countPerfect(N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<4>) {
4fd800b3a8 2011-02-23        kinaba: 	int N = 28;
4fd800b3a8 2011-02-23        kinaba: 	int K = 41;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal = 1599;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, SquareFreeSets().countPerfect(N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<5>) {
4fd800b3a8 2011-02-23        kinaba: 	int N = 500;
4fd800b3a8 2011-02-23        kinaba: 	int K = 500;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal = 59964104;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, SquareFreeSets().countPerfect(N, K)); }
4fd800b3a8 2011-02-23        kinaba: int Test_(Case_<6>) {
4fd800b3a8 2011-02-23        kinaba: 	int N = 100;
4fd800b3a8 2011-02-23        kinaba: 	int K = 1;
4fd800b3a8 2011-02-23        kinaba: 	int RetVal = 60;
4fd800b3a8 2011-02-23        kinaba: 	return verify_case(RetVal, SquareFreeSets().countPerfect(N, K)); }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
4fd800b3a8 2011-02-23        kinaba: template<>      void Run_<-1>() {}
4fd800b3a8 2011-02-23        kinaba: int main() { Run_<0>(); }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE
4fd800b3a8 2011-02-23        kinaba: