f79e63c2fd 2016-05-26        kinaba: #include <iostream>
f79e63c2fd 2016-05-26        kinaba: #include <sstream>
f79e63c2fd 2016-05-26        kinaba: #include <iomanip>
f79e63c2fd 2016-05-26        kinaba: #include <vector>
f79e63c2fd 2016-05-26        kinaba: #include <string>
f79e63c2fd 2016-05-26        kinaba: #include <map>
f79e63c2fd 2016-05-26        kinaba: #include <set>
f79e63c2fd 2016-05-26        kinaba: #include <algorithm>
f79e63c2fd 2016-05-26        kinaba: #include <numeric>
f79e63c2fd 2016-05-26        kinaba: #include <iterator>
f79e63c2fd 2016-05-26        kinaba: #include <functional>
f79e63c2fd 2016-05-26        kinaba: #include <complex>
f79e63c2fd 2016-05-26        kinaba: #include <queue>
f79e63c2fd 2016-05-26        kinaba: #include <stack>
f79e63c2fd 2016-05-26        kinaba: #include <cmath>
f79e63c2fd 2016-05-26        kinaba: #include <cassert>
f79e63c2fd 2016-05-26        kinaba: #include <tuple>
f79e63c2fd 2016-05-26        kinaba: using namespace std;
f79e63c2fd 2016-05-26        kinaba: typedef long long LL;
f79e63c2fd 2016-05-26        kinaba: typedef complex<double> CMP;
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: class LCMGCD { public:
f79e63c2fd 2016-05-26        kinaba: 	string isPossible(vector <int> x, int t)
f79e63c2fd 2016-05-26        kinaba: 	{
f79e63c2fd 2016-05-26        kinaba: 		pair<int,int> tt = crack(t);
f79e63c2fd 2016-05-26        kinaba: 		vector<pair<int,int>> ab;
f79e63c2fd 2016-05-26        kinaba: 		for(int xi: x) {
f79e63c2fd 2016-05-26        kinaba: 			pair<int, int> xx = crack(xi);
f79e63c2fd 2016-05-26        kinaba: 			ab.emplace_back(sign(xx.first, tt.first), sign(xx.second, tt.second));
f79e63c2fd 2016-05-26        kinaba: 		}
f79e63c2fd 2016-05-26        kinaba: 		return solve(ab) ? "Possible" : "Impossible";
f79e63c2fd 2016-05-26        kinaba: 	}
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: 	pair<int,int> crack(int x)
f79e63c2fd 2016-05-26        kinaba: 	{
f79e63c2fd 2016-05-26        kinaba: 		int a=0, b=0;
f79e63c2fd 2016-05-26        kinaba: 		while(x%2==0) x/=2, a++;
f79e63c2fd 2016-05-26        kinaba: 		while(x%3==0) x/=3, b++;
f79e63c2fd 2016-05-26        kinaba: 		return make_pair(a,b);
f79e63c2fd 2016-05-26        kinaba: 	}
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: 	int sign(int x, int t)
f79e63c2fd 2016-05-26        kinaba: 	{
f79e63c2fd 2016-05-26        kinaba: 		return x<t ? 0 : x==t ? 1 : 2;
f79e63c2fd 2016-05-26        kinaba: 	}
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: 	// can we make (1,1) by max and min?
f79e63c2fd 2016-05-26        kinaba: 	bool solve(vector<pair<int,int>> x)
f79e63c2fd 2016-05-26        kinaba: 	{
f79e63c2fd 2016-05-26        kinaba: 		set<vector<int>> vis;
f79e63c2fd 2016-05-26        kinaba: 		vector<int> sig(7);
f79e63c2fd 2016-05-26        kinaba: 		vis.insert(sig);
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: 		for(auto ab: x) {
f79e63c2fd 2016-05-26        kinaba: 			int s = ab.first*3 + ab.second;
f79e63c2fd 2016-05-26        kinaba: 			if(0<s&&s<8)
f79e63c2fd 2016-05-26        kinaba: 				if(sig[s-1]<5)
f79e63c2fd 2016-05-26        kinaba: 					sig[s-1]++;
f79e63c2fd 2016-05-26        kinaba: 		}
f79e63c2fd 2016-05-26        kinaba: 		goal = vector<int>(7); goal[3]=1;
f79e63c2fd 2016-05-26        kinaba: 		return rec(sig, vis);
f79e63c2fd 2016-05-26        kinaba: 	}
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: 	vector<int> goal;
f79e63c2fd 2016-05-26        kinaba: 	bool rec(vector<int>& sig, set<vector<int>>& vis)
f79e63c2fd 2016-05-26        kinaba: 	{
f79e63c2fd 2016-05-26        kinaba: 		if(sig[3] >= 2)
f79e63c2fd 2016-05-26        kinaba: 			return true;
f79e63c2fd 2016-05-26        kinaba: 		if(sig == goal)
f79e63c2fd 2016-05-26        kinaba: 			return true;
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: 		if(vis.count(sig))
f79e63c2fd 2016-05-26        kinaba: 			return false;
f79e63c2fd 2016-05-26        kinaba: 		vis.insert(sig);
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: 		for(int a=1; a<8; ++a) if(sig[a-1])
f79e63c2fd 2016-05-26        kinaba: 		for(int b=a; b<8; ++b) if(sig[b-1]) {
f79e63c2fd 2016-05-26        kinaba: 			if(b==a && sig[a-1]==1) continue;
f79e63c2fd 2016-05-26        kinaba: 			sig[a-1]--;
f79e63c2fd 2016-05-26        kinaba: 			sig[b-1]--;
f79e63c2fd 2016-05-26        kinaba: 			int z = max(a/3,b/3)*3 + max(a%3,b%3);
f79e63c2fd 2016-05-26        kinaba: 			if(0<z && z<8) {
f79e63c2fd 2016-05-26        kinaba: 				sig[z-1]++;
f79e63c2fd 2016-05-26        kinaba: 				if(rec(sig, vis)) return true;
f79e63c2fd 2016-05-26        kinaba: 				sig[z-1]--;
f79e63c2fd 2016-05-26        kinaba: 			} else {
f79e63c2fd 2016-05-26        kinaba: 				if(rec(sig, vis)) return true;
f79e63c2fd 2016-05-26        kinaba: 			}
f79e63c2fd 2016-05-26        kinaba: 			z = min(a/3,b/3)*3 + min(a%3,b%3);
f79e63c2fd 2016-05-26        kinaba: 			if(0<z && z<8) {
f79e63c2fd 2016-05-26        kinaba: 				sig[z-1]++;
f79e63c2fd 2016-05-26        kinaba: 				if(rec(sig, vis)) return true;
f79e63c2fd 2016-05-26        kinaba: 				sig[z-1]--;
f79e63c2fd 2016-05-26        kinaba: 			} else {
f79e63c2fd 2016-05-26        kinaba: 				if(rec(sig, vis)) return true;
f79e63c2fd 2016-05-26        kinaba: 			}
f79e63c2fd 2016-05-26        kinaba: 			sig[a-1]++;
f79e63c2fd 2016-05-26        kinaba: 			sig[b-1]++;
f79e63c2fd 2016-05-26        kinaba: 		}
f79e63c2fd 2016-05-26        kinaba: 		return false;
f79e63c2fd 2016-05-26        kinaba: 	}
f79e63c2fd 2016-05-26        kinaba: };
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: // BEGIN CUT HERE
f79e63c2fd 2016-05-26        kinaba: #include <ctime>
f79e63c2fd 2016-05-26        kinaba: double start_time; string timer()
f79e63c2fd 2016-05-26        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
f79e63c2fd 2016-05-26        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
f79e63c2fd 2016-05-26        kinaba:  { os << "{ ";
f79e63c2fd 2016-05-26        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
f79e63c2fd 2016-05-26        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
f79e63c2fd 2016-05-26        kinaba: void verify_case(const string& Expected, const string& Received) {
f79e63c2fd 2016-05-26        kinaba:  bool ok = (Expected == Received);
f79e63c2fd 2016-05-26        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
f79e63c2fd 2016-05-26        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
f79e63c2fd 2016-05-26        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
f79e63c2fd 2016-05-26        kinaba: #define END	 verify_case(_, LCMGCD().isPossible(x, t));}
f79e63c2fd 2016-05-26        kinaba: int main(){
f79e63c2fd 2016-05-26        kinaba: 
f79e63c2fd 2016-05-26        kinaba: CASE(0)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {2,3};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 6;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Possible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(1)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {4,9};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 6;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Impossible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(2)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {6,12,24,18,36,72,54,108,216};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 36;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Possible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(3)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {6,27,81,729};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 6;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Impossible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(4)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
f79e63c2fd 2016-05-26        kinaba:  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 1;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Possible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(5)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {72,16,16,16,16,16,27,27,27,27,27,27,27,27,27};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 72;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Possible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(6)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {100663296, 544195584, 229582512, 59049};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 60466176;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Possible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(7)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {2,4,8,16,32,64};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 256;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Impossible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(8)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {6,9};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 6;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Impossible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(9)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,
f79e63c2fd 2016-05-26        kinaba: 	18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 6;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Impossible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(8)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {6,6,9};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 6;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Possible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: CASE(8)
f79e63c2fd 2016-05-26        kinaba: 	int x_[] = {9,18,12};
f79e63c2fd 2016-05-26        kinaba: 	  vector <int> x(x_, x_+sizeof(x_)/sizeof(*x_));
f79e63c2fd 2016-05-26        kinaba: 	int t = 6;
f79e63c2fd 2016-05-26        kinaba: 	string _ = "Possible";
f79e63c2fd 2016-05-26        kinaba: END
f79e63c2fd 2016-05-26        kinaba: }
f79e63c2fd 2016-05-26        kinaba: // END CUT HERE