d921147eef 2012-07-01        kinaba: #include <iostream>
d921147eef 2012-07-01        kinaba: #include <sstream>
d921147eef 2012-07-01        kinaba: #include <iomanip>
d921147eef 2012-07-01        kinaba: #include <vector>
d921147eef 2012-07-01        kinaba: #include <string>
d921147eef 2012-07-01        kinaba: #include <map>
d921147eef 2012-07-01        kinaba: #include <set>
d921147eef 2012-07-01        kinaba: #include <algorithm>
d921147eef 2012-07-01        kinaba: #include <numeric>
d921147eef 2012-07-01        kinaba: #include <iterator>
d921147eef 2012-07-01        kinaba: #include <functional>
d921147eef 2012-07-01        kinaba: #include <complex>
d921147eef 2012-07-01        kinaba: #include <queue>
d921147eef 2012-07-01        kinaba: #include <stack>
d921147eef 2012-07-01        kinaba: #include <cmath>
d921147eef 2012-07-01        kinaba: #include <cassert>
d921147eef 2012-07-01        kinaba: using namespace std;
d921147eef 2012-07-01        kinaba: typedef long long LL;
d921147eef 2012-07-01        kinaba: typedef long double LD;
d921147eef 2012-07-01        kinaba: typedef complex<LD> CMP;
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: class RectangularSum { public:
d921147eef 2012-07-01        kinaba: 	long long minimalArea(int height_, int width_, long long S)
d921147eef 2012-07-01        kinaba: 	{
d921147eef 2012-07-01        kinaba: 		LL H = height_;
d921147eef 2012-07-01        kinaba: 		LL W = width_;
d921147eef 2012-07-01        kinaba: 		static const LL INF = 0x7fffffffffffffffLL;
d921147eef 2012-07-01        kinaba: 		LL best = INF;
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: 		vector<LL> divs;
d921147eef 2012-07-01        kinaba: 		for(LL x=1; x*x<=2*S; ++x)
d921147eef 2012-07-01        kinaba: 			if(2*S%x==0) {
d921147eef 2012-07-01        kinaba: 				divs.push_back(x);
d921147eef 2012-07-01        kinaba: 				divs.push_back(2*S/x);
d921147eef 2012-07-01        kinaba: 			}
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: 		// sum = L1 + (L1 + wX) + (L1 + 2wX) + ... + (L1 + (Y-1)wX)
d921147eef 2012-07-01        kinaba: 		//     = L1*Y + wX(Y-1)Y/2
d921147eef 2012-07-01        kinaba: 		//     = (L1+wX(Y-1)/2) * Y
d921147eef 2012-07-01        kinaba: 		// L1 = p + (p+1) + ... + (p+X-1)
d921147eef 2012-07-01        kinaba: 		//    = p*X + X(X-1)/2
d921147eef 2012-07-01        kinaba: 		//
d921147eef 2012-07-01        kinaba: 		// sum = (p + (X-1)/2 + w(Y-1)/2) * X * Y
d921147eef 2012-07-01        kinaba: 		// 2sum = (2p + X-1 + w(Y-1)) * X * Y
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: 		for(int i=0; i<divs.size(); ++i) {
d921147eef 2012-07-01        kinaba: 			LL Y = divs[i];
d921147eef 2012-07-01        kinaba: 			if(Y<=H)
d921147eef 2012-07-01        kinaba: 			{
d921147eef 2012-07-01        kinaba: 				LL R = (2*S)/Y;
d921147eef 2012-07-01        kinaba: 				for(int j=0; j<divs.size(); ++j) {
d921147eef 2012-07-01        kinaba: 					LL X = divs[j];
d921147eef 2012-07-01        kinaba: 					if(X<=W && R%X == 0)
d921147eef 2012-07-01        kinaba: 					{
d921147eef 2012-07-01        kinaba: 						LL T = R/X;
d921147eef 2012-07-01        kinaba: 						LL twoP = T - (X-1) - W*(Y-1);
d921147eef 2012-07-01        kinaba: 						if( (twoP&1) == 1 )
d921147eef 2012-07-01        kinaba: 							continue;
d921147eef 2012-07-01        kinaba: 						LL P = twoP/2;
d921147eef 2012-07-01        kinaba: 						if( P<0 || H*W<=P )
d921147eef 2012-07-01        kinaba: 							continue;
d921147eef 2012-07-01        kinaba: 						LL x = P%W;
d921147eef 2012-07-01        kinaba: 						LL y = P/W;
d921147eef 2012-07-01        kinaba: 						if( x+X<=W && y+Y<=H ) {
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: 							best = min(best, X*Y);
d921147eef 2012-07-01        kinaba: 						}
d921147eef 2012-07-01        kinaba: 					}
d921147eef 2012-07-01        kinaba: 				}
d921147eef 2012-07-01        kinaba: 			}
d921147eef 2012-07-01        kinaba: 		}
d921147eef 2012-07-01        kinaba: 		return best == INF ? -1 : best;
d921147eef 2012-07-01        kinaba: 	}
d921147eef 2012-07-01        kinaba: };
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: // BEGIN CUT HERE
d921147eef 2012-07-01        kinaba: #include <ctime>
d921147eef 2012-07-01        kinaba: double start_time; string timer()
d921147eef 2012-07-01        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
d921147eef 2012-07-01        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
d921147eef 2012-07-01        kinaba:  { os << "{ ";
d921147eef 2012-07-01        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
d921147eef 2012-07-01        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
d921147eef 2012-07-01        kinaba: void verify_case(const long long& Expected, const long long& Received) {
d921147eef 2012-07-01        kinaba:  bool ok = (Expected == Received);
d921147eef 2012-07-01        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
d921147eef 2012-07-01        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
d921147eef 2012-07-01        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
d921147eef 2012-07-01        kinaba: #define END	 verify_case(_, RectangularSum().minimalArea(height, width, S));}
d921147eef 2012-07-01        kinaba: int main(){
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: CASE(0)
d921147eef 2012-07-01        kinaba: 	int height = 2;
d921147eef 2012-07-01        kinaba: 	int width = 3;
d921147eef 2012-07-01        kinaba: 	long long S = 8LL;
d921147eef 2012-07-01        kinaba: 	long long _ = 4LL;
d921147eef 2012-07-01        kinaba: END
d921147eef 2012-07-01        kinaba: CASE(1)
d921147eef 2012-07-01        kinaba: 	int height = 3;
d921147eef 2012-07-01        kinaba: 	int width = 3;
d921147eef 2012-07-01        kinaba: 	long long S = 10LL;
d921147eef 2012-07-01        kinaba: 	long long _ = -1LL;
d921147eef 2012-07-01        kinaba: END
d921147eef 2012-07-01        kinaba: CASE(2)
d921147eef 2012-07-01        kinaba: 	int height = 3;
d921147eef 2012-07-01        kinaba: 	int width = 3;
d921147eef 2012-07-01        kinaba: 	long long S = 36LL;
d921147eef 2012-07-01        kinaba: 	long long _ = 9LL;
d921147eef 2012-07-01        kinaba: END
d921147eef 2012-07-01        kinaba: CASE(3)
d921147eef 2012-07-01        kinaba: 	int height = 25;
d921147eef 2012-07-01        kinaba: 	int width = 25;
d921147eef 2012-07-01        kinaba: 	long long S = 16000LL;
d921147eef 2012-07-01        kinaba: 	long long _ = 32LL;
d921147eef 2012-07-01        kinaba: END
d921147eef 2012-07-01        kinaba: CASE(4)
d921147eef 2012-07-01        kinaba: 	int height = 1000000;
d921147eef 2012-07-01        kinaba: 	int width = 1000000;
d921147eef 2012-07-01        kinaba: 	long long S = 1000000000000LL;
d921147eef 2012-07-01        kinaba: 	long long _ = 2LL;
d921147eef 2012-07-01        kinaba: END
d921147eef 2012-07-01        kinaba: CASE(5)
d921147eef 2012-07-01        kinaba: 	int height = 1000000;
d921147eef 2012-07-01        kinaba: 	int width = 1000000;
d921147eef 2012-07-01        kinaba: 	long long S = 123456789LL;
d921147eef 2012-07-01        kinaba: 	long long _ = -999LL;
d921147eef 2012-07-01        kinaba: END
d921147eef 2012-07-01        kinaba: CASE(6)
d921147eef 2012-07-01        kinaba: 	int height = 2;
d921147eef 2012-07-01        kinaba: 	int width = 3;
d921147eef 2012-07-01        kinaba: 	long long S = 6LL;
d921147eef 2012-07-01        kinaba: 	long long _ = 4LL;
d921147eef 2012-07-01        kinaba: END
d921147eef 2012-07-01        kinaba: 
d921147eef 2012-07-01        kinaba: }
d921147eef 2012-07-01        kinaba: // END CUT HERE