c009363094 2013-04-06        kinaba: #include <iostream>
c009363094 2013-04-06        kinaba: #include <sstream>
c009363094 2013-04-06        kinaba: #include <iomanip>
c009363094 2013-04-06        kinaba: #include <vector>
c009363094 2013-04-06        kinaba: #include <string>
c009363094 2013-04-06        kinaba: #include <map>
c009363094 2013-04-06        kinaba: #include <set>
c009363094 2013-04-06        kinaba: #include <algorithm>
c009363094 2013-04-06        kinaba: #include <numeric>
c009363094 2013-04-06        kinaba: #include <iterator>
c009363094 2013-04-06        kinaba: #include <functional>
c009363094 2013-04-06        kinaba: #include <complex>
c009363094 2013-04-06        kinaba: #include <queue>
c009363094 2013-04-06        kinaba: #include <stack>
c009363094 2013-04-06        kinaba: #include <cmath>
c009363094 2013-04-06        kinaba: #include <cassert>
c009363094 2013-04-06        kinaba: using namespace std;
c009363094 2013-04-06        kinaba: typedef long long LL;
c009363094 2013-04-06        kinaba: typedef long double LD;
c009363094 2013-04-06        kinaba: typedef complex<LD> CMP;
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: class ThePowers { public:
c009363094 2013-04-06        kinaba: 	long long find(int A, int B)
c009363094 2013-04-06        kinaba: 	{
c009363094 2013-04-06        kinaba: 		LL total = 1;
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: 		int prev_cnt = 1;
c009363094 2013-04-06        kinaba: 		for(int K=31; K>=1; --K)
c009363094 2013-04-06        kinaba: 		{
c009363094 2013-04-06        kinaba: 			int ub = invpow(A,K);
c009363094 2013-04-06        kinaba: 			int cnt = num_ppprime_under(ub);
c009363094 2013-04-06        kinaba: 			LL x = solve2(K,B) * (cnt - prev_cnt);
c009363094 2013-04-06        kinaba: 			total += x;
c009363094 2013-04-06        kinaba: 			prev_cnt = cnt;
c009363094 2013-04-06        kinaba: 		}
c009363094 2013-04-06        kinaba: 		return total;
c009363094 2013-04-06        kinaba: 	}
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: 	// max x s.t. x^K <= A;
c009363094 2013-04-06        kinaba: 	int invpow(int A, int K)
c009363094 2013-04-06        kinaba: 	{
c009363094 2013-04-06        kinaba: 		int v = 0;
c009363094 2013-04-06        kinaba: 		int c = (int)pow(A, 1.0/K);
c009363094 2013-04-06        kinaba: 		for(int x=max(1,c-3); x<=c+3; ++x)
c009363094 2013-04-06        kinaba: 			if( pow_leq(x, K, A) )
c009363094 2013-04-06        kinaba: 				v = x;
c009363094 2013-04-06        kinaba: 		return v;
c009363094 2013-04-06        kinaba: 	}
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: 	// number of non-square, cubic, ... numbers in [1,N]
c009363094 2013-04-06        kinaba: 	int num_ppprime_under(int N)
c009363094 2013-04-06        kinaba: 	{
c009363094 2013-04-06        kinaba: 		int total = N;
c009363094 2013-04-06        kinaba: 		vector<int> num(32);
c009363094 2013-04-06        kinaba: 		for(int p=num.size()-1; p>=2; --p)
c009363094 2013-04-06        kinaba: 		{
c009363094 2013-04-06        kinaba: 			num[p] = invpow(N, p) - 1;
c009363094 2013-04-06        kinaba: 			for(int q=p+p; q<num.size(); q+=p)
c009363094 2013-04-06        kinaba: 				num[p] -= num[q];
c009363094 2013-04-06        kinaba: 			total -= num[p];
c009363094 2013-04-06        kinaba: 		}
c009363094 2013-04-06        kinaba: 		return total;
c009363094 2013-04-06        kinaba: 	}
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: 	int pow_leq(int x, int p, int N)
c009363094 2013-04-06        kinaba: 	{
c009363094 2013-04-06        kinaba: 		LL v = 1;
c009363094 2013-04-06        kinaba: 		for(int i=0; i<p; ++i) {
c009363094 2013-04-06        kinaba: 			v *= x;
c009363094 2013-04-06        kinaba: 			if(v>N)
c009363094 2013-04-06        kinaba: 				return false;
c009363094 2013-04-06        kinaba: 		}
c009363094 2013-04-06        kinaba: 		return true;
c009363094 2013-04-06        kinaba: 	}
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: 	// number of [1,K]*[1,B]
c009363094 2013-04-06        kinaba: 	LL solve2(int K, int B)
c009363094 2013-04-06        kinaba: 	{
c009363094 2013-04-06        kinaba: 		set<LL> test;
c009363094 2013-04-06        kinaba: 		for(LL x=1; x<=K; ++x)
c009363094 2013-04-06        kinaba: 		for(LL y=1; y<=B; ++y)
c009363094 2013-04-06        kinaba: 			test.insert(x*y);
c009363094 2013-04-06        kinaba: 		return test.size();
c009363094 2013-04-06        kinaba: 	}
c009363094 2013-04-06        kinaba: };
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: // BEGIN CUT HERE
c009363094 2013-04-06        kinaba: #include <ctime>
c009363094 2013-04-06        kinaba: double start_time; string timer()
c009363094 2013-04-06        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
c009363094 2013-04-06        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
c009363094 2013-04-06        kinaba:  { os << "{ ";
c009363094 2013-04-06        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
c009363094 2013-04-06        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
c009363094 2013-04-06        kinaba: void verify_case(const long long& Expected, const long long& Received) {
c009363094 2013-04-06        kinaba:  bool ok = (Expected == Received);
c009363094 2013-04-06        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
c009363094 2013-04-06        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
c009363094 2013-04-06        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
c009363094 2013-04-06        kinaba: #define END	 verify_case(_, ThePowers().find(A, B));}
c009363094 2013-04-06        kinaba: int main(){
c009363094 2013-04-06        kinaba: 
c009363094 2013-04-06        kinaba: CASE(0)
c009363094 2013-04-06        kinaba: 	int A = 7;
c009363094 2013-04-06        kinaba: 	int B = 4;
c009363094 2013-04-06        kinaba: 	long long _ = 23LL;
c009363094 2013-04-06        kinaba: END
c009363094 2013-04-06        kinaba: CASE(1)
c009363094 2013-04-06        kinaba: 	int A = 1;
c009363094 2013-04-06        kinaba: 	int B = 1;
c009363094 2013-04-06        kinaba: 	long long _ = 1LL;
c009363094 2013-04-06        kinaba: END
c009363094 2013-04-06        kinaba: CASE(2)
c009363094 2013-04-06        kinaba: 	int A = 1000000000;
c009363094 2013-04-06        kinaba: 	int B = 1000000000;
c009363094 2013-04-06        kinaba: 	long long _ = 999983644283653287LL;
c009363094 2013-04-06        kinaba: END
c009363094 2013-04-06        kinaba: CASE(3)
c009363094 2013-04-06        kinaba: 	int A = 999999999;
c009363094 2013-04-06        kinaba: 	int B = 5;
c009363094 2013-04-06        kinaba: 	long long _ = 4999934406LL;
c009363094 2013-04-06        kinaba: END
c009363094 2013-04-06        kinaba: /*
c009363094 2013-04-06        kinaba: CASE(4)
c009363094 2013-04-06        kinaba: 	int A = ;
c009363094 2013-04-06        kinaba: 	int B = ;
c009363094 2013-04-06        kinaba: 	long long _ = LL;
c009363094 2013-04-06        kinaba: END
c009363094 2013-04-06        kinaba: CASE(5)
c009363094 2013-04-06        kinaba: 	int A = ;
c009363094 2013-04-06        kinaba: 	int B = ;
c009363094 2013-04-06        kinaba: 	long long _ = LL;
c009363094 2013-04-06        kinaba: END
c009363094 2013-04-06        kinaba: */
c009363094 2013-04-06        kinaba: }
c009363094 2013-04-06        kinaba: // END CUT HERE