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 LL MODVAL = 1000000009;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: LL ADD(LL x, LL y) { return (x+y)%MODVAL; }
4fd800b3a8 2011-02-23        kinaba: LL SUB(LL x, LL y) { return (x-y+MODVAL)%MODVAL; }
4fd800b3a8 2011-02-23        kinaba: LL MUL(LL x, LL y) { return (x*y)%MODVAL; }
4fd800b3a8 2011-02-23        kinaba: LL POW(LL x, LL e) {
4fd800b3a8 2011-02-23        kinaba: 	LL v = 1;
4fd800b3a8 2011-02-23        kinaba: 	for(;e;x=MUL(x,x),e>>=1)
4fd800b3a8 2011-02-23        kinaba: 		if(e&1)
4fd800b3a8 2011-02-23        kinaba: 			v = MUL(v, x);
4fd800b3a8 2011-02-23        kinaba: 	return v;
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: LL DIV(LL x, LL y) { return MUL(x, POW(y, MODVAL-2)); }
4fd800b3a8 2011-02-23        kinaba: LL C_impl(LL n, LL k) {
4fd800b3a8 2011-02-23        kinaba: 	LL v = 1;
4fd800b3a8 2011-02-23        kinaba: 	for(LL i=1; i<=k; ++i)
4fd800b3a8 2011-02-23        kinaba: 		v = DIV(MUL(v, n-i+1), i);
4fd800b3a8 2011-02-23        kinaba: 	return v;
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: LL C_tbl[40][40];
4fd800b3a8 2011-02-23        kinaba: LL C(LL n, LL k) {
4fd800b3a8 2011-02-23        kinaba: 	if( C_tbl[n][k] < 0 )
4fd800b3a8 2011-02-23        kinaba: 		C_tbl[n][k] = C_impl(n,k);
4fd800b3a8 2011-02-23        kinaba: 	return C_tbl[n][k];
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: class RooksParty { public:
4fd800b3a8 2011-02-23        kinaba: 	int countArrangements(int rows, int columns, vector <int> counts)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		for(int n=0;n<40;++n)
4fd800b3a8 2011-02-23        kinaba: 			for(int k=0;k<40;++k)
4fd800b3a8 2011-02-23        kinaba: 				C_tbl[n][k] = -1;
4fd800b3a8 2011-02-23        kinaba: 		sort(counts.rbegin(), counts.rend());
4fd800b3a8 2011-02-23        kinaba: 		return (int)rec(rows, columns, counts, 0);
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 	map<pair<pair<int,int>,int>, LL> memo;
4fd800b3a8 2011-02-23        kinaba: 	LL rec(int H, int W, vector<int>& counts, int i)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if( i == counts.size() )
4fd800b3a8 2011-02-23        kinaba: 			return 1;
4fd800b3a8 2011-02-23        kinaba: 		int n = counts[i];
4fd800b3a8 2011-02-23        kinaba: 		if( H*W < n )
4fd800b3a8 2011-02-23        kinaba: 			return 0;
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		if(H>W)
4fd800b3a8 2011-02-23        kinaba: 			swap(H,W);
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		pair<pair<int,int>,int> key(make_pair(H,W),i);
4fd800b3a8 2011-02-23        kinaba: 		if( memo.count(key) )
4fd800b3a8 2011-02-23        kinaba: 			return memo[key];
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		LL cnt = 0;
4fd800b3a8 2011-02-23        kinaba: 		for(int h=1; h<=min(H,n); ++h)
4fd800b3a8 2011-02-23        kinaba: 			for(int w=1; w<=min(W,n); ++w)
4fd800b3a8 2011-02-23        kinaba: 				if( h*w >= n )
4fd800b3a8 2011-02-23        kinaba: 					cnt = ADD(cnt, MUL(MUL(C(H,h), C(W,w)), MUL(count(h,w,n),rec(H-h,W-w,counts,i+1))));
4fd800b3a8 2011-02-23        kinaba: 		return memo[key] = cnt;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	map<pair<pair<int,int>,int>, LL> memo2;
4fd800b3a8 2011-02-23        kinaba: 	LL count(int h, int w, int n)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if( h*w < n )
4fd800b3a8 2011-02-23        kinaba: 			return 0;
4fd800b3a8 2011-02-23        kinaba: 		pair<pair<int,int>,int> key(make_pair(h,w),n);
4fd800b3a8 2011-02-23        kinaba: 		if(memo2.count(key))
4fd800b3a8 2011-02-23        kinaba: 			return memo2[key];
4fd800b3a8 2011-02-23        kinaba: 		LL cnt = freedom(h,w,n);
4fd800b3a8 2011-02-23        kinaba: 		for(int t=1; t<=w-1; ++t)
4fd800b3a8 2011-02-23        kinaba: 			cnt = SUB(cnt, MUL(count(h,w-t,n),C(w,t)));
4fd800b3a8 2011-02-23        kinaba: 		return memo2[key] = cnt;
4fd800b3a8 2011-02-23        kinaba: 	}
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 	map<pair<pair<int,int>,int>, LL> memo3;
4fd800b3a8 2011-02-23        kinaba: 	LL freedom(int h, int w, int n)
4fd800b3a8 2011-02-23        kinaba: 	{
4fd800b3a8 2011-02-23        kinaba: 		if(h*w<n) return 0;
4fd800b3a8 2011-02-23        kinaba: 		//if(h>n)   return 0;
4fd800b3a8 2011-02-23        kinaba: 		if(h==0)  return 1;
4fd800b3a8 2011-02-23        kinaba: 		pair<pair<int,int>,int> key(make_pair(h,w),n);
4fd800b3a8 2011-02-23        kinaba: 		if(memo3.count(key))
4fd800b3a8 2011-02-23        kinaba: 			return memo3[key];
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: 		LL cnt = 0;
4fd800b3a8 2011-02-23        kinaba: 		for(int t=0; t<=min(n,w); ++t)
4fd800b3a8 2011-02-23        kinaba: 			cnt = ADD(cnt, MUL(freedom(h-1, w, n-t), C(w,t)));
4fd800b3a8 2011-02-23        kinaba: 		return memo3[key]=cnt;
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()
4fd800b3a8 2011-02-23        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
4fd800b3a8 2011-02-23        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
4fd800b3a8 2011-02-23        kinaba:  { os << "{ ";
4fd800b3a8 2011-02-23        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
4fd800b3a8 2011-02-23        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
4fd800b3a8 2011-02-23        kinaba: void verify_case(const int& Expected, const int& Received) {
4fd800b3a8 2011-02-23        kinaba:  bool ok = (Expected == Received);
4fd800b3a8 2011-02-23        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
4fd800b3a8 2011-02-23        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
4fd800b3a8 2011-02-23        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
4fd800b3a8 2011-02-23        kinaba: #define END	 verify_case(_, RooksParty().countArrangements(rows, columns, counts));}
4fd800b3a8 2011-02-23        kinaba: int main(){
4fd800b3a8 2011-02-23        kinaba: 
4fd800b3a8 2011-02-23        kinaba: CASE(0)
4fd800b3a8 2011-02-23        kinaba: 	int rows = 2;
4fd800b3a8 2011-02-23        kinaba: 	int columns = 3;
4fd800b3a8 2011-02-23        kinaba: 	int counts_[] = {1,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> counts(counts_, counts_+sizeof(counts_)/sizeof(*counts_));
4fd800b3a8 2011-02-23        kinaba: 	int _ = 12;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(1)
4fd800b3a8 2011-02-23        kinaba: 	int rows = 5;
4fd800b3a8 2011-02-23        kinaba: 	int columns = 2;
4fd800b3a8 2011-02-23        kinaba: 	int counts_[] = {3};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> counts(counts_, counts_+sizeof(counts_)/sizeof(*counts_));
4fd800b3a8 2011-02-23        kinaba: 	int _ = 120;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(2)
4fd800b3a8 2011-02-23        kinaba: 	int rows = 5;
4fd800b3a8 2011-02-23        kinaba: 	int columns = 2;
4fd800b3a8 2011-02-23        kinaba: 	int counts_[] = {1,1,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> counts(counts_, counts_+sizeof(counts_)/sizeof(*counts_));
4fd800b3a8 2011-02-23        kinaba: 	int _ = 0;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(3)
4fd800b3a8 2011-02-23        kinaba: 	int rows = 8;
4fd800b3a8 2011-02-23        kinaba: 	int columns = 8;
4fd800b3a8 2011-02-23        kinaba: 	int counts_[] = {1,1,1,1,1,1,1,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> counts(counts_, counts_+sizeof(counts_)/sizeof(*counts_));
4fd800b3a8 2011-02-23        kinaba: 	int _ = 625702391;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(4)
4fd800b3a8 2011-02-23        kinaba: 	int rows = 4;
4fd800b3a8 2011-02-23        kinaba: 	int columns = 2;
4fd800b3a8 2011-02-23        kinaba: 	int counts_[] = {3,1};
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> counts(counts_, counts_+sizeof(counts_)/sizeof(*counts_));
4fd800b3a8 2011-02-23        kinaba: 	int _ = 8;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: /*
4fd800b3a8 2011-02-23        kinaba: CASE(5)
4fd800b3a8 2011-02-23        kinaba: 	int rows = ;
4fd800b3a8 2011-02-23        kinaba: 	int columns = ;
4fd800b3a8 2011-02-23        kinaba: 	int counts_[] = ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> counts(counts_, counts_+sizeof(counts_)/sizeof(*counts_));
4fd800b3a8 2011-02-23        kinaba: 	int _ = ;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: CASE(6)
4fd800b3a8 2011-02-23        kinaba: 	int rows = ;
4fd800b3a8 2011-02-23        kinaba: 	int columns = ;
4fd800b3a8 2011-02-23        kinaba: 	int counts_[] = ;
4fd800b3a8 2011-02-23        kinaba: 	  vector <int> counts(counts_, counts_+sizeof(counts_)/sizeof(*counts_));
4fd800b3a8 2011-02-23        kinaba: 	int _ = ;
4fd800b3a8 2011-02-23        kinaba: END
4fd800b3a8 2011-02-23        kinaba: */
4fd800b3a8 2011-02-23        kinaba: }
4fd800b3a8 2011-02-23        kinaba: // END CUT HERE