109f2a9050 2012-09-08        kinaba: #include <iostream>
109f2a9050 2012-09-08        kinaba: #include <sstream>
109f2a9050 2012-09-08        kinaba: #include <iomanip>
109f2a9050 2012-09-08        kinaba: #include <vector>
109f2a9050 2012-09-08        kinaba: #include <string>
109f2a9050 2012-09-08        kinaba: #include <map>
109f2a9050 2012-09-08        kinaba: #include <set>
109f2a9050 2012-09-08        kinaba: #include <algorithm>
109f2a9050 2012-09-08        kinaba: #include <numeric>
109f2a9050 2012-09-08        kinaba: #include <iterator>
109f2a9050 2012-09-08        kinaba: #include <functional>
109f2a9050 2012-09-08        kinaba: #include <complex>
109f2a9050 2012-09-08        kinaba: #include <queue>
109f2a9050 2012-09-08        kinaba: #include <stack>
109f2a9050 2012-09-08        kinaba: #include <cmath>
109f2a9050 2012-09-08        kinaba: #include <cassert>
109f2a9050 2012-09-08        kinaba: using namespace std;
109f2a9050 2012-09-08        kinaba: typedef long long LL;
109f2a9050 2012-09-08        kinaba: typedef long double LD;
109f2a9050 2012-09-08        kinaba: typedef complex<LD> CMP;
109f2a9050 2012-09-08        kinaba: 
109f2a9050 2012-09-08        kinaba: static const unsigned MODVAL = 555555555;
109f2a9050 2012-09-08        kinaba: struct mint
109f2a9050 2012-09-08        kinaba: {
109f2a9050 2012-09-08        kinaba: 	unsigned val;
109f2a9050 2012-09-08        kinaba: 	mint():val(0){}
109f2a9050 2012-09-08        kinaba: 	mint(int      x):val(x%MODVAL) {}
109f2a9050 2012-09-08        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
109f2a9050 2012-09-08        kinaba: 	mint(LL       x):val(x%MODVAL) {}
109f2a9050 2012-09-08        kinaba: };
109f2a9050 2012-09-08        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
109f2a9050 2012-09-08        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
109f2a9050 2012-09-08        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
109f2a9050 2012-09-08        kinaba: mint operator+(mint x, mint y) { return x+=y; }
109f2a9050 2012-09-08        kinaba: mint operator-(mint x, mint y) { return x-=y; }
109f2a9050 2012-09-08        kinaba: mint operator*(mint x, mint y) { return x*=y; }
109f2a9050 2012-09-08        kinaba: mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
109f2a9050 2012-09-08        kinaba: 
109f2a9050 2012-09-08        kinaba: vector< vector<mint> > CP_;
109f2a9050 2012-09-08        kinaba: mint C(LL n, LL k) {
109f2a9050 2012-09-08        kinaba: 	while( CP_.size() <= n ) {
109f2a9050 2012-09-08        kinaba: 		int nn = CP_.size();
109f2a9050 2012-09-08        kinaba: 		CP_.push_back(vector<mint>(nn+1,1));
109f2a9050 2012-09-08        kinaba: 		for(int kk=1; kk<nn; ++kk)
109f2a9050 2012-09-08        kinaba: 			CP_[nn][kk] = CP_[nn-1][kk-1] + CP_[nn-1][kk];
109f2a9050 2012-09-08        kinaba: 	}
109f2a9050 2012-09-08        kinaba: 	return k<0 || n<k ? 0 : CP_[n][k];
109f2a9050 2012-09-08        kinaba: }
109f2a9050 2012-09-08        kinaba: 
109f2a9050 2012-09-08        kinaba: class XorBoard { public:
109f2a9050 2012-09-08        kinaba: 	int count(int H, int W, int Rcount, int Ccount, int S)
109f2a9050 2012-09-08        kinaba: 	{
109f2a9050 2012-09-08        kinaba: 		vector<mint> xx(W+1), yy(H+1);
109f2a9050 2012-09-08        kinaba: 		for(int x=0; x<=W; ++x)
109f2a9050 2012-09-08        kinaba: 			xx[x] = subProblem(W, Ccount, x);
109f2a9050 2012-09-08        kinaba: 		for(int y=0; y<=H; ++y)
109f2a9050 2012-09-08        kinaba: 			yy[y] = subProblem(H, Rcount, y);
109f2a9050 2012-09-08        kinaba: 
109f2a9050 2012-09-08        kinaba: 		mint cnt = 0;
109f2a9050 2012-09-08        kinaba: 		for(int x=0; x<=W; ++x)
109f2a9050 2012-09-08        kinaba: 		for(int y=0; y<=H; ++y)
109f2a9050 2012-09-08        kinaba: 			if( x*(H-y)+(W-x)*y == S )
109f2a9050 2012-09-08        kinaba: 				cnt += xx[x]*yy[y];
109f2a9050 2012-09-08        kinaba: 		return cnt.val;
109f2a9050 2012-09-08        kinaba: 	}
109f2a9050 2012-09-08        kinaba: 
109f2a9050 2012-09-08        kinaba: 	mint subProblem(int Z, int T, int k)
109f2a9050 2012-09-08        kinaba: 	{
109f2a9050 2012-09-08        kinaba: 		// Z objects
109f2a9050 2012-09-08        kinaba: 		// T flips
109f2a9050 2012-09-08        kinaba: 		// k of them flipped odd # of times
109f2a9050 2012-09-08        kinaba: 		// Z-k even
109f2a9050 2012-09-08        kinaba: 		if( T < k )
109f2a9050 2012-09-08        kinaba: 			return 0;
109f2a9050 2012-09-08        kinaba: 		T -= k;
109f2a9050 2012-09-08        kinaba: 		if( T%2 != 0 )
109f2a9050 2012-09-08        kinaba: 			return 0;
109f2a9050 2012-09-08        kinaba: 		T /= 2;
109f2a9050 2012-09-08        kinaba: 		mint cc = C(Z, k);
109f2a9050 2012-09-08        kinaba: 		// Z obj
109f2a9050 2012-09-08        kinaba: 		// T flips
109f2a9050 2012-09-08        kinaba: 		return cc * C(T+Z-1, Z-1);
109f2a9050 2012-09-08        kinaba: 	}
109f2a9050 2012-09-08        kinaba: };
109f2a9050 2012-09-08        kinaba: 
109f2a9050 2012-09-08        kinaba: // BEGIN CUT HERE
109f2a9050 2012-09-08        kinaba: #include <ctime>
109f2a9050 2012-09-08        kinaba: double start_time; string timer()
109f2a9050 2012-09-08        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
109f2a9050 2012-09-08        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
109f2a9050 2012-09-08        kinaba:  { os << "{ ";
109f2a9050 2012-09-08        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
109f2a9050 2012-09-08        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
109f2a9050 2012-09-08        kinaba: void verify_case(const int& Expected, const int& Received) {
109f2a9050 2012-09-08        kinaba:  bool ok = (Expected == Received);
109f2a9050 2012-09-08        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
109f2a9050 2012-09-08        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
109f2a9050 2012-09-08        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
109f2a9050 2012-09-08        kinaba: #define END	 verify_case(_, XorBoard().count(H, W, Rcount, Ccount, S));}
109f2a9050 2012-09-08        kinaba: int main(){
109f2a9050 2012-09-08        kinaba: 
109f2a9050 2012-09-08        kinaba: CASE(0)
109f2a9050 2012-09-08        kinaba: 	int H = 2;
109f2a9050 2012-09-08        kinaba: 	int W = 2;
109f2a9050 2012-09-08        kinaba: 	int Rcount = 2;
109f2a9050 2012-09-08        kinaba: 	int Ccount = 2;
109f2a9050 2012-09-08        kinaba: 	int S = 4;
109f2a9050 2012-09-08        kinaba: 	int _ = 4;
109f2a9050 2012-09-08        kinaba: END
109f2a9050 2012-09-08        kinaba: CASE(1)
109f2a9050 2012-09-08        kinaba: 	int H = 2;
109f2a9050 2012-09-08        kinaba: 	int W = 2;
109f2a9050 2012-09-08        kinaba: 	int Rcount = 0;
109f2a9050 2012-09-08        kinaba: 	int Ccount = 0;
109f2a9050 2012-09-08        kinaba: 	int S = 1;
109f2a9050 2012-09-08        kinaba: 	int _ = 0;
109f2a9050 2012-09-08        kinaba: END
109f2a9050 2012-09-08        kinaba: CASE(2)
109f2a9050 2012-09-08        kinaba: 	int H = 10;
109f2a9050 2012-09-08        kinaba: 	int W = 20;
109f2a9050 2012-09-08        kinaba: 	int Rcount = 50;
109f2a9050 2012-09-08        kinaba: 	int Ccount = 40;
109f2a9050 2012-09-08        kinaba: 	int S = 200;
109f2a9050 2012-09-08        kinaba: 	int _ = 333759825;
109f2a9050 2012-09-08        kinaba: END
109f2a9050 2012-09-08        kinaba: CASE(3)
109f2a9050 2012-09-08        kinaba: 	int H = 1200;
109f2a9050 2012-09-08        kinaba: 	int W = 1000;
109f2a9050 2012-09-08        kinaba: 	int Rcount = 800;
109f2a9050 2012-09-08        kinaba: 	int Ccount = 600;
109f2a9050 2012-09-08        kinaba: 	int S = 4000;
109f2a9050 2012-09-08        kinaba: 	int _ = 96859710;
109f2a9050 2012-09-08        kinaba: END
109f2a9050 2012-09-08        kinaba: CASE(4)
109f2a9050 2012-09-08        kinaba: 	int H = 555;
109f2a9050 2012-09-08        kinaba: 	int W = 555;
109f2a9050 2012-09-08        kinaba: 	int Rcount = 555;
109f2a9050 2012-09-08        kinaba: 	int Ccount = 555;
109f2a9050 2012-09-08        kinaba: 	int S = 5550;
109f2a9050 2012-09-08        kinaba: 	int _ = 549361755;
109f2a9050 2012-09-08        kinaba: END
109f2a9050 2012-09-08        kinaba: CASE(5)
109f2a9050 2012-09-08        kinaba: 	int H = 1555;
109f2a9050 2012-09-08        kinaba: 	int W = 1555;
109f2a9050 2012-09-08        kinaba: 	int Rcount = 755;
109f2a9050 2012-09-08        kinaba: 	int Ccount = 755;
109f2a9050 2012-09-08        kinaba: 	int S = 555555;
109f2a9050 2012-09-08        kinaba: 	int _ = -1;
109f2a9050 2012-09-08        kinaba: END
109f2a9050 2012-09-08        kinaba: /*
109f2a9050 2012-09-08        kinaba: CASE(6)
109f2a9050 2012-09-08        kinaba: 	int H = ;
109f2a9050 2012-09-08        kinaba: 	int W = ;
109f2a9050 2012-09-08        kinaba: 	int Rcount = ;
109f2a9050 2012-09-08        kinaba: 	int Ccount = ;
109f2a9050 2012-09-08        kinaba: 	int S = ;
109f2a9050 2012-09-08        kinaba: 	int _ = ;
109f2a9050 2012-09-08        kinaba: END
109f2a9050 2012-09-08        kinaba: */
109f2a9050 2012-09-08        kinaba: }
109f2a9050 2012-09-08        kinaba: // END CUT HERE