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Artifact 2562ed8ee62d4add232a95ab5e8c786a91780b26


#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<LD> CMP;

static const int MODVAL = 1234567891;
struct mint
{
	unsigned val;
	mint():val(0){}
	mint(int      x):val(x%MODVAL) {}
	mint(unsigned x):val(x%MODVAL) {}
	mint(LL       x):val(x%MODVAL) {}
};
mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
mint operator+(mint x, mint y) { return x+=y; }
mint operator-(mint x, mint y) { return x-=y; }
mint operator*(mint x, mint y) { return x*=y; }

template<typename T>
vector<T> MATMUL(const vector< vector<T> >& a, const vector<T>& v)
{
	int N = a.size();
	vector<T> u(N);
	for(int i=0; i<N; ++i)
	for(int j=0; j<N; ++j)
		u[i] += a[i][j]*v[j];
	return u;
}

template<typename T>
vector< vector<T> > MATMUL(const vector< vector<T> >& a, const vector< vector<T> >& b)
{
	int N = a.size();
	vector< vector<T> > c(N, vector<T>(N));
	for(int i=0; i<N; ++i)
	for(int j=0; j<N; ++j)
	for(int k=0; k<N; ++k)
		c[i][j] += a[i][k]*b[k][j];
	return c;
}

template<typename T>
vector< vector<T> > MATPOW(vector< vector<T> > a, LL e)
{
	int N = a.size();
	vector< vector<T> > c(N, vector<T>(N));
	for(int i=0; i<N; ++i) c[i][i] = 1;
	for(; e; e>>=1) {
		if(e&1)
			c = MATMUL(c, a);
		a = MATMUL(a, a);
	}
	return c;
}

class TheBrickTowerHardDivOne { public:
	int find(int C, int K, long long H)
	{
		vector< vector<int> > patterns;
		{
			vector<int> p;
			vector<bool> used(4);
			generate_patterns(true, 4, used, p, 0, patterns);
		}
		const vector<int> compress = calc_compress_table(patterns).first;
		const vector<bool> is_repr = calc_compress_table(patterns).second;

		const int PN = patterns.size();
		const int CPN = *max_element(compress.begin(), compress.end())+1;
		const int D = CPN * (K+1);

		vector< vector<mint> > m(D+1, vector<mint>(D+1));
		for(int pa=0; pa<PN; ++pa) if(is_repr[pa])
		for(int pb=0; pb<PN; ++pb) {
			vector<mint> tt = transition(patterns[pa], patterns[pb], K, C);
			for(int ka=0; ka<=K; ++ka)
			for(int kt=0; kt<=K; ++kt) {
				int kb = ka + kt + internal(patterns[pb]);
				if(kb <= K)
					m[compress[pb]*(K+1)+kb][compress[pa]*(K+1)+ka] += tt[kt];
			}
		}
		for(int x=0; x<D+1; ++x)
			m[D][x] = 1;

		vector<mint> v(D+1);
		for(int pa=0; pa<PN; ++pa) {
			int ka = internal(patterns[pa]);
			if(ka <= K)
				v[compress[pa]*(K+1)+ka] += counting(patterns[pa], C);
		}

		v = MATMUL(MATPOW(m, H-1), v);
		return accumulate(v.begin(), v.end(), mint(0)).val;
	}

	// TODO: auto generate.
	pair< vector<int>, vector<bool> >
		calc_compress_table(const vector< vector<int> >& patterns)
	{
		// {0}         00,00
		// {1,2,5,9}   00,01
		// {3,6}       00,11
		// {4,7,12,13} 00,12
		// {8}         01,10
		// {10,11}     01,12
		// {14}        01,23
		vector<int> repr(patterns.size());
		vector<bool> is_repr(patterns.size(), false);
		is_repr[0] = true; repr[0] = 0;
		is_repr[1] = true; repr[1] = repr[2] = repr[5] = repr[9] = 1;
		is_repr[3] = true; repr[3] = repr[6] = 2;
		is_repr[4] = true; repr[4] = repr[7] = repr[12] = repr[13] = 3;
		is_repr[8] = true; repr[8] = 4;
		is_repr[10] = true; repr[10] = repr[11] = 5;
		is_repr[14] = true; repr[14] = 6;
		return make_pair(repr, is_repr);
	}

	mint counting(const vector<int>& p, int C)
	{
		return counting(set<int>(p.begin(), p.end()).size(), C);
	}

	mint counting(int N, int C)
	{
		if(C<0)
			return 0;
		mint v = 1;
		for(int i=0; i<N; ++i)
			v *= (C-i);
		return v;
	}

	int internal(const vector<int>& p)
	{
		return (p[0]==p[1])+(p[1]==p[3])+(p[3]==p[2])+(p[2]==p[0]);
	}

	vector<mint> transition(const vector<int>& pa, const vector<int>& pb, int K, int C)
	{
		const int AN = set<int>(pa.begin(), pa.end()).size();
		const int BN = set<int>(pb.begin(), pb.end()).size();

		vector< vector<int> > patterns;
		{
			vector<int> p;
			vector<bool> used(AN+BN, false);
			generate_patterns(false, BN, used, p, AN, patterns);
		}

		vector<mint> answer(K+1);
		for(int i=0; i<patterns.size(); ++i) {
			const vector<int>& p = patterns[i];
			int k = 0;
			for(int x=0; x<4; ++x) k += (pa[x]==p[pb[x]]);
			
			if(k <= K) {
				int N = max(*max_element(p.begin(), p.end()) - (AN-1), 0);
				answer[k] += counting(N, C-AN);
			}
		}
		return answer;
	}

	void generate_patterns(bool ALLOW_DUP, int LEN, vector<bool>& used,
	                       vector<int>& p, int next, vector< vector<int> >& patterns)
	{
		if(p.size() == LEN)
			patterns.push_back(p);
		else
			for(int v=0; v<=next; ++v) if(ALLOW_DUP || !used[v]) {
				p.push_back(v);
				used[v] = true;
				generate_patterns(ALLOW_DUP, LEN, used, p, max(v+1, next), patterns);
				used[v] = false;
				p.pop_back();
			}
	}
};

// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
 { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
 { os << "{ ";
   for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
   os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
 bool ok = (Expected == Received);
 if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
 cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END	 verify_case(_, TheBrickTowerHardDivOne().find(C, K, H));}
int main(){
CASE(0)
	int C = 2; 
	int K = 0; 
	long long H = 2LL; 
	int _ = 4; 
END
CASE(2)
	int C = 2; 
	int K = 3; 
	long long H = 1LL; 
	int _ = 14; 
END
CASE(3)
	int C = 4; 
	int K = 7; 
	long long H = 47LL; 
	int _ = 1008981254; 
END
CASE(4)
	int C = 4747; 
	int K = 7; 
	long long H = 474747474747474747LL; 
	int _ = 473182063; 
END
}
// END CUT HERE