0ea7f42c5c 2012-09-02        kinaba: #include <iostream>
0ea7f42c5c 2012-09-02        kinaba: #include <sstream>
0ea7f42c5c 2012-09-02        kinaba: #include <iomanip>
0ea7f42c5c 2012-09-02        kinaba: #include <vector>
0ea7f42c5c 2012-09-02        kinaba: #include <string>
0ea7f42c5c 2012-09-02        kinaba: #include <map>
0ea7f42c5c 2012-09-02        kinaba: #include <set>
0ea7f42c5c 2012-09-02        kinaba: #include <algorithm>
0ea7f42c5c 2012-09-02        kinaba: #include <numeric>
0ea7f42c5c 2012-09-02        kinaba: #include <iterator>
0ea7f42c5c 2012-09-02        kinaba: #include <functional>
0ea7f42c5c 2012-09-02        kinaba: #include <complex>
0ea7f42c5c 2012-09-02        kinaba: #include <queue>
0ea7f42c5c 2012-09-02        kinaba: #include <stack>
0ea7f42c5c 2012-09-02        kinaba: #include <cmath>
0ea7f42c5c 2012-09-02        kinaba: #include <cassert>
0ea7f42c5c 2012-09-02        kinaba: using namespace std;
0ea7f42c5c 2012-09-02        kinaba: typedef long long LL;
0ea7f42c5c 2012-09-02        kinaba: typedef long double LD;
0ea7f42c5c 2012-09-02        kinaba: typedef complex<LD> CMP;
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: static const int MODVAL = 1234567891;
0ea7f42c5c 2012-09-02        kinaba: struct mint
0ea7f42c5c 2012-09-02        kinaba: {
0ea7f42c5c 2012-09-02        kinaba: 	unsigned val;
0ea7f42c5c 2012-09-02        kinaba: 	mint():val(0){}
0ea7f42c5c 2012-09-02        kinaba: 	mint(int      x):val(x%MODVAL) {}
0ea7f42c5c 2012-09-02        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
0ea7f42c5c 2012-09-02        kinaba: 	mint(LL       x):val(x%MODVAL) {}
0ea7f42c5c 2012-09-02        kinaba: };
0ea7f42c5c 2012-09-02        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
0ea7f42c5c 2012-09-02        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
0ea7f42c5c 2012-09-02        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
0ea7f42c5c 2012-09-02        kinaba: mint operator+(mint x, mint y) { return x+=y; }
0ea7f42c5c 2012-09-02        kinaba: mint operator-(mint x, mint y) { return x-=y; }
0ea7f42c5c 2012-09-02        kinaba: mint operator*(mint x, mint y) { return x*=y; }
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: template<typename T>
0ea7f42c5c 2012-09-02        kinaba: vector<T> MATMUL(const vector< vector<T> >& a, const vector<T>& v)
0ea7f42c5c 2012-09-02        kinaba: {
0ea7f42c5c 2012-09-02        kinaba: 	int N = a.size();
0ea7f42c5c 2012-09-02        kinaba: 	vector<T> u(N);
0ea7f42c5c 2012-09-02        kinaba: 	for(int i=0; i<N; ++i)
0ea7f42c5c 2012-09-02        kinaba: 	for(int j=0; j<N; ++j)
0ea7f42c5c 2012-09-02        kinaba: 		u[i] += a[i][j]*v[j];
0ea7f42c5c 2012-09-02        kinaba: 	return u;
0ea7f42c5c 2012-09-02        kinaba: }
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: template<typename T>
0ea7f42c5c 2012-09-02        kinaba: vector< vector<T> > MATMUL(const vector< vector<T> >& a, const vector< vector<T> >& b)
0ea7f42c5c 2012-09-02        kinaba: {
0ea7f42c5c 2012-09-02        kinaba: 	int N = a.size();
0ea7f42c5c 2012-09-02        kinaba: 	vector< vector<T> > c(N, vector<T>(N));
0ea7f42c5c 2012-09-02        kinaba: 	for(int i=0; i<N; ++i)
0ea7f42c5c 2012-09-02        kinaba: 	for(int j=0; j<N; ++j)
0ea7f42c5c 2012-09-02        kinaba: 	for(int k=0; k<N; ++k)
0ea7f42c5c 2012-09-02        kinaba: 		c[i][j] += a[i][k]*b[k][j];
0ea7f42c5c 2012-09-02        kinaba: 	return c;
0ea7f42c5c 2012-09-02        kinaba: }
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: template<typename T>
0ea7f42c5c 2012-09-02        kinaba: vector< vector<T> > MATPOW(vector< vector<T> > a, LL e)
0ea7f42c5c 2012-09-02        kinaba: {
0ea7f42c5c 2012-09-02        kinaba: 	int N = a.size();
0ea7f42c5c 2012-09-02        kinaba: 	vector< vector<T> > c(N, vector<T>(N));
0ea7f42c5c 2012-09-02        kinaba: 	for(int i=0; i<N; ++i) c[i][i] = 1;
0ea7f42c5c 2012-09-02        kinaba: 	for(; e; e>>=1) {
0ea7f42c5c 2012-09-02        kinaba: 		if(e&1)
0ea7f42c5c 2012-09-02        kinaba: 			c = MATMUL(c, a);
0ea7f42c5c 2012-09-02        kinaba: 		a = MATMUL(a, a);
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: 	return c;
0ea7f42c5c 2012-09-02        kinaba: }
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: class TheBrickTowerHardDivOne { public:
0ea7f42c5c 2012-09-02        kinaba: 	int find(int C, int K, long long H)
0ea7f42c5c 2012-09-02        kinaba: 	{
0ea7f42c5c 2012-09-02        kinaba: 		vector< vector<int> > patterns;
0ea7f42c5c 2012-09-02        kinaba: 		{
0ea7f42c5c 2012-09-02        kinaba: 			vector<int> p;
0ea7f42c5c 2012-09-02        kinaba: 			vector<bool> used(4);
0ea7f42c5c 2012-09-02        kinaba: 			generate_patterns(true, 4, used, p, 0, patterns);
0ea7f42c5c 2012-09-02        kinaba: 		}
0ea7f42c5c 2012-09-02        kinaba: 		const vector<int> compress = calc_compress_table(patterns).first;
0ea7f42c5c 2012-09-02        kinaba: 		const vector<bool> is_repr = calc_compress_table(patterns).second;
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 		const int PN = patterns.size();
0ea7f42c5c 2012-09-02        kinaba: 		const int CPN = *max_element(compress.begin(), compress.end())+1;
0ea7f42c5c 2012-09-02        kinaba: 		const int D = CPN * (K+1);
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 		vector< vector<mint> > m(D+1, vector<mint>(D+1));
0ea7f42c5c 2012-09-02        kinaba: 		for(int pa=0; pa<PN; ++pa) if(is_repr[pa])
0ea7f42c5c 2012-09-02        kinaba: 		for(int pb=0; pb<PN; ++pb) {
0ea7f42c5c 2012-09-02        kinaba: 			vector<mint> tt = transition(patterns[pa], patterns[pb], K, C);
0ea7f42c5c 2012-09-02        kinaba: 			for(int ka=0; ka<=K; ++ka)
0ea7f42c5c 2012-09-02        kinaba: 			for(int kt=0; kt<=K; ++kt) {
0ea7f42c5c 2012-09-02        kinaba: 				int kb = ka + kt + internal(patterns[pb]);
0ea7f42c5c 2012-09-02        kinaba: 				if(kb <= K)
0ea7f42c5c 2012-09-02        kinaba: 					m[compress[pb]*(K+1)+kb][compress[pa]*(K+1)+ka] += tt[kt];
0ea7f42c5c 2012-09-02        kinaba: 			}
0ea7f42c5c 2012-09-02        kinaba: 		}
0ea7f42c5c 2012-09-02        kinaba: 		for(int x=0; x<D+1; ++x)
0ea7f42c5c 2012-09-02        kinaba: 			m[D][x] = 1;
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 		vector<mint> v(D+1);
0ea7f42c5c 2012-09-02        kinaba: 		for(int pa=0; pa<PN; ++pa) {
0ea7f42c5c 2012-09-02        kinaba: 			int ka = internal(patterns[pa]);
0ea7f42c5c 2012-09-02        kinaba: 			if(ka <= K)
0ea7f42c5c 2012-09-02        kinaba: 				v[compress[pa]*(K+1)+ka] += counting(patterns[pa], C);
0ea7f42c5c 2012-09-02        kinaba: 		}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 		v = MATMUL(MATPOW(m, H-1), v);
0ea7f42c5c 2012-09-02        kinaba: 		return accumulate(v.begin(), v.end(), mint(0)).val;
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 	// TODO: auto generate.
0ea7f42c5c 2012-09-02        kinaba: 	pair< vector<int>, vector<bool> >
0ea7f42c5c 2012-09-02        kinaba: 		calc_compress_table(const vector< vector<int> >& patterns)
0ea7f42c5c 2012-09-02        kinaba: 	{
0ea7f42c5c 2012-09-02        kinaba: 		// {0}         00,00
0ea7f42c5c 2012-09-02        kinaba: 		// {1,2,5,9}   00,01
0ea7f42c5c 2012-09-02        kinaba: 		// {3,6}       00,11
0ea7f42c5c 2012-09-02        kinaba: 		// {4,7,12,13} 00,12
0ea7f42c5c 2012-09-02        kinaba: 		// {8}         01,10
0ea7f42c5c 2012-09-02        kinaba: 		// {10,11}     01,12
0ea7f42c5c 2012-09-02        kinaba: 		// {14}        01,23
0ea7f42c5c 2012-09-02        kinaba: 		vector<int> repr(patterns.size());
0ea7f42c5c 2012-09-02        kinaba: 		vector<bool> is_repr(patterns.size(), false);
0ea7f42c5c 2012-09-02        kinaba: 		is_repr[0] = true; repr[0] = 0;
0ea7f42c5c 2012-09-02        kinaba: 		is_repr[1] = true; repr[1] = repr[2] = repr[5] = repr[9] = 1;
0ea7f42c5c 2012-09-02        kinaba: 		is_repr[3] = true; repr[3] = repr[6] = 2;
0ea7f42c5c 2012-09-02        kinaba: 		is_repr[4] = true; repr[4] = repr[7] = repr[12] = repr[13] = 3;
0ea7f42c5c 2012-09-02        kinaba: 		is_repr[8] = true; repr[8] = 4;
0ea7f42c5c 2012-09-02        kinaba: 		is_repr[10] = true; repr[10] = repr[11] = 5;
0ea7f42c5c 2012-09-02        kinaba: 		is_repr[14] = true; repr[14] = 6;
0ea7f42c5c 2012-09-02        kinaba: 		return make_pair(repr, is_repr);
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 	mint counting(const vector<int>& p, int C)
0ea7f42c5c 2012-09-02        kinaba: 	{
0ea7f42c5c 2012-09-02        kinaba: 		return counting(set<int>(p.begin(), p.end()).size(), C);
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 	mint counting(int N, int C)
0ea7f42c5c 2012-09-02        kinaba: 	{
0ea7f42c5c 2012-09-02        kinaba: 		if(C<0)
0ea7f42c5c 2012-09-02        kinaba: 			return 0;
0ea7f42c5c 2012-09-02        kinaba: 		mint v = 1;
0ea7f42c5c 2012-09-02        kinaba: 		for(int i=0; i<N; ++i)
0ea7f42c5c 2012-09-02        kinaba: 			v *= (C-i);
0ea7f42c5c 2012-09-02        kinaba: 		return v;
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 	int internal(const vector<int>& p)
0ea7f42c5c 2012-09-02        kinaba: 	{
0ea7f42c5c 2012-09-02        kinaba: 		return (p[0]==p[1])+(p[1]==p[3])+(p[3]==p[2])+(p[2]==p[0]);
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 	vector<mint> transition(const vector<int>& pa, const vector<int>& pb, int K, int C)
0ea7f42c5c 2012-09-02        kinaba: 	{
0ea7f42c5c 2012-09-02        kinaba: 		const int AN = set<int>(pa.begin(), pa.end()).size();
0ea7f42c5c 2012-09-02        kinaba: 		const int BN = set<int>(pb.begin(), pb.end()).size();
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 		vector< vector<int> > patterns;
0ea7f42c5c 2012-09-02        kinaba: 		{
0ea7f42c5c 2012-09-02        kinaba: 			vector<int> p;
0ea7f42c5c 2012-09-02        kinaba: 			vector<bool> used(AN+BN, false);
0ea7f42c5c 2012-09-02        kinaba: 			generate_patterns(false, BN, used, p, AN, patterns);
0ea7f42c5c 2012-09-02        kinaba: 		}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 		vector<mint> answer(K+1);
0ea7f42c5c 2012-09-02        kinaba: 		for(int i=0; i<patterns.size(); ++i) {
0ea7f42c5c 2012-09-02        kinaba: 			const vector<int>& p = patterns[i];
0ea7f42c5c 2012-09-02        kinaba: 			int k = 0;
0ea7f42c5c 2012-09-02        kinaba: 			for(int x=0; x<4; ++x) k += (pa[x]==p[pb[x]]);
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 			if(k <= K) {
0ea7f42c5c 2012-09-02        kinaba: 				int N = max(*max_element(p.begin(), p.end()) - (AN-1), 0);
0ea7f42c5c 2012-09-02        kinaba: 				answer[k] += counting(N, C-AN);
0ea7f42c5c 2012-09-02        kinaba: 			}
0ea7f42c5c 2012-09-02        kinaba: 		}
0ea7f42c5c 2012-09-02        kinaba: 		return answer;
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: 	void generate_patterns(bool ALLOW_DUP, int LEN, vector<bool>& used,
0ea7f42c5c 2012-09-02        kinaba: 	                       vector<int>& p, int next, vector< vector<int> >& patterns)
0ea7f42c5c 2012-09-02        kinaba: 	{
0ea7f42c5c 2012-09-02        kinaba: 		if(p.size() == LEN)
0ea7f42c5c 2012-09-02        kinaba: 			patterns.push_back(p);
0ea7f42c5c 2012-09-02        kinaba: 		else
0ea7f42c5c 2012-09-02        kinaba: 			for(int v=0; v<=next; ++v) if(ALLOW_DUP || !used[v]) {
0ea7f42c5c 2012-09-02        kinaba: 				p.push_back(v);
0ea7f42c5c 2012-09-02        kinaba: 				used[v] = true;
0ea7f42c5c 2012-09-02        kinaba: 				generate_patterns(ALLOW_DUP, LEN, used, p, max(v+1, next), patterns);
0ea7f42c5c 2012-09-02        kinaba: 				used[v] = false;
0ea7f42c5c 2012-09-02        kinaba: 				p.pop_back();
0ea7f42c5c 2012-09-02        kinaba: 			}
0ea7f42c5c 2012-09-02        kinaba: 	}
0ea7f42c5c 2012-09-02        kinaba: };
0ea7f42c5c 2012-09-02        kinaba: 
0ea7f42c5c 2012-09-02        kinaba: // BEGIN CUT HERE
0ea7f42c5c 2012-09-02        kinaba: #include <ctime>
0ea7f42c5c 2012-09-02        kinaba: double start_time; string timer()
0ea7f42c5c 2012-09-02        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
0ea7f42c5c 2012-09-02        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
0ea7f42c5c 2012-09-02        kinaba:  { os << "{ ";
0ea7f42c5c 2012-09-02        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
0ea7f42c5c 2012-09-02        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
0ea7f42c5c 2012-09-02        kinaba: void verify_case(const int& Expected, const int& Received) {
0ea7f42c5c 2012-09-02        kinaba:  bool ok = (Expected == Received);
0ea7f42c5c 2012-09-02        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
0ea7f42c5c 2012-09-02        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
0ea7f42c5c 2012-09-02        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
0ea7f42c5c 2012-09-02        kinaba: #define END	 verify_case(_, TheBrickTowerHardDivOne().find(C, K, H));}
0ea7f42c5c 2012-09-02        kinaba: int main(){
0ea7f42c5c 2012-09-02        kinaba: CASE(0)
0ea7f42c5c 2012-09-02        kinaba: 	int C = 2;
0ea7f42c5c 2012-09-02        kinaba: 	int K = 0;
0ea7f42c5c 2012-09-02        kinaba: 	long long H = 2LL;
0ea7f42c5c 2012-09-02        kinaba: 	int _ = 4;
0ea7f42c5c 2012-09-02        kinaba: END
0ea7f42c5c 2012-09-02        kinaba: CASE(2)
0ea7f42c5c 2012-09-02        kinaba: 	int C = 2;
0ea7f42c5c 2012-09-02        kinaba: 	int K = 3;
0ea7f42c5c 2012-09-02        kinaba: 	long long H = 1LL;
0ea7f42c5c 2012-09-02        kinaba: 	int _ = 14;
0ea7f42c5c 2012-09-02        kinaba: END
0ea7f42c5c 2012-09-02        kinaba: CASE(3)
0ea7f42c5c 2012-09-02        kinaba: 	int C = 4;
0ea7f42c5c 2012-09-02        kinaba: 	int K = 7;
0ea7f42c5c 2012-09-02        kinaba: 	long long H = 47LL;
0ea7f42c5c 2012-09-02        kinaba: 	int _ = 1008981254;
0ea7f42c5c 2012-09-02        kinaba: END
0ea7f42c5c 2012-09-02        kinaba: CASE(4)
0ea7f42c5c 2012-09-02        kinaba: 	int C = 4747;
0ea7f42c5c 2012-09-02        kinaba: 	int K = 7;
0ea7f42c5c 2012-09-02        kinaba: 	long long H = 474747474747474747LL;
0ea7f42c5c 2012-09-02        kinaba: 	int _ = 473182063;
0ea7f42c5c 2012-09-02        kinaba: END
0ea7f42c5c 2012-09-02        kinaba: }
0ea7f42c5c 2012-09-02        kinaba: // END CUT HERE