fa7992ffc5 2012-08-06        kinaba: #include <iostream>
fa7992ffc5 2012-08-06        kinaba: #include <sstream>
fa7992ffc5 2012-08-06        kinaba: #include <iomanip>
fa7992ffc5 2012-08-06        kinaba: #include <vector>
fa7992ffc5 2012-08-06        kinaba: #include <string>
fa7992ffc5 2012-08-06        kinaba: #include <map>
fa7992ffc5 2012-08-06        kinaba: #include <set>
fa7992ffc5 2012-08-06        kinaba: #include <algorithm>
fa7992ffc5 2012-08-06        kinaba: #include <numeric>
fa7992ffc5 2012-08-06        kinaba: #include <iterator>
fa7992ffc5 2012-08-06        kinaba: #include <functional>
fa7992ffc5 2012-08-06        kinaba: #include <complex>
fa7992ffc5 2012-08-06        kinaba: #include <queue>
fa7992ffc5 2012-08-06        kinaba: #include <stack>
fa7992ffc5 2012-08-06        kinaba: #include <cmath>
fa7992ffc5 2012-08-06        kinaba: #include <cassert>
fa7992ffc5 2012-08-06        kinaba: using namespace std;
fa7992ffc5 2012-08-06        kinaba: typedef long long LL;
fa7992ffc5 2012-08-06        kinaba: typedef long double LD;
fa7992ffc5 2012-08-06        kinaba: typedef complex<LD> CMP;
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: static const int MODVAL = 1000000007;
fa7992ffc5 2012-08-06        kinaba: struct mint
fa7992ffc5 2012-08-06        kinaba: {
fa7992ffc5 2012-08-06        kinaba: 	int val;
fa7992ffc5 2012-08-06        kinaba: 	mint():val(0){}
fa7992ffc5 2012-08-06        kinaba: 	mint(int    x):val(x%MODVAL) {}
fa7992ffc5 2012-08-06        kinaba: 	mint(size_t x):val(x%MODVAL) {}
fa7992ffc5 2012-08-06        kinaba: 	mint(LL     x):val(x%MODVAL) {}
fa7992ffc5 2012-08-06        kinaba: };
fa7992ffc5 2012-08-06        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
fa7992ffc5 2012-08-06        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
fa7992ffc5 2012-08-06        kinaba: mint operator+(mint x, mint y) { return x+=y; }
fa7992ffc5 2012-08-06        kinaba: mint operator*(mint x, mint y) { return x*=y; }
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: template<typename T>
fa7992ffc5 2012-08-06        kinaba: vector<T> MATMUL(const vector< vector<T> >& a, const vector<T>& v)
fa7992ffc5 2012-08-06        kinaba: {
fa7992ffc5 2012-08-06        kinaba: 	int N = a.size();
fa7992ffc5 2012-08-06        kinaba: 	vector<T> u(N);
fa7992ffc5 2012-08-06        kinaba: 	for(int i=0; i<N; ++i)
fa7992ffc5 2012-08-06        kinaba: 	for(int j=0; j<N; ++j)
fa7992ffc5 2012-08-06        kinaba: 		u[i] += a[i][j]*v[j];
fa7992ffc5 2012-08-06        kinaba: 	return u;
fa7992ffc5 2012-08-06        kinaba: }
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: template<typename T>
fa7992ffc5 2012-08-06        kinaba: vector< vector<T> > MATMUL(const vector< vector<T> >& a, const vector< vector<T> >& b)
fa7992ffc5 2012-08-06        kinaba: {
fa7992ffc5 2012-08-06        kinaba: 	int N = a.size();
fa7992ffc5 2012-08-06        kinaba: 	vector< vector<T> > c(N, vector<T>(N));
fa7992ffc5 2012-08-06        kinaba: 	for(int i=0; i<N; ++i)
fa7992ffc5 2012-08-06        kinaba: 	for(int j=0; j<N; ++j)
fa7992ffc5 2012-08-06        kinaba: 	for(int k=0; k<N; ++k)
fa7992ffc5 2012-08-06        kinaba: 		c[i][j] += a[i][k]*b[k][j];
fa7992ffc5 2012-08-06        kinaba: 	return c;
fa7992ffc5 2012-08-06        kinaba: }
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: template<typename T>
fa7992ffc5 2012-08-06        kinaba: vector< vector<T> > MATPOW(vector< vector<T> > a, LL e)
fa7992ffc5 2012-08-06        kinaba: {
fa7992ffc5 2012-08-06        kinaba: 	int N = a.size();
fa7992ffc5 2012-08-06        kinaba: 	vector< vector<T> > c(N, vector<T>(N));
fa7992ffc5 2012-08-06        kinaba: 	for(int i=0; i<N; ++i) c[i][i] = 1;
fa7992ffc5 2012-08-06        kinaba: 	for(; e; e>>=1) {
fa7992ffc5 2012-08-06        kinaba: 		if(e&1)
fa7992ffc5 2012-08-06        kinaba: 			c = MATMUL(c, a);
fa7992ffc5 2012-08-06        kinaba: 		a = MATMUL(a, a);
fa7992ffc5 2012-08-06        kinaba: 	}
fa7992ffc5 2012-08-06        kinaba: 	return c;
fa7992ffc5 2012-08-06        kinaba: }
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: class ConversionMachine { public:
fa7992ffc5 2012-08-06        kinaba: 	int countAll(string word1, string word2, vector <int> costs, int maxCost)
fa7992ffc5 2012-08-06        kinaba: 	{
fa7992ffc5 2012-08-06        kinaba: 		int d[3] = {};
fa7992ffc5 2012-08-06        kinaba: 		LL minCost = 0;
fa7992ffc5 2012-08-06        kinaba: 		for(int i=0; i<word1.size(); ++i) {
fa7992ffc5 2012-08-06        kinaba: 			int dd=0;
fa7992ffc5 2012-08-06        kinaba: 			while( word1[i] != word2[i] ) {
fa7992ffc5 2012-08-06        kinaba: 				dd      += 1;
fa7992ffc5 2012-08-06        kinaba: 				minCost += costs[word1[i]-'a'];
fa7992ffc5 2012-08-06        kinaba: 				word1[i] = (word1[i]+1-'a')%3 + 'a';
fa7992ffc5 2012-08-06        kinaba: 			}
fa7992ffc5 2012-08-06        kinaba: 			d[dd] += 1;
fa7992ffc5 2012-08-06        kinaba: 		}
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: 		if( minCost > maxCost )
fa7992ffc5 2012-08-06        kinaba: 			return 0;
fa7992ffc5 2012-08-06        kinaba: 		LL c3 = accumulate(costs.begin(), costs.end(), 0LL);
fa7992ffc5 2012-08-06        kinaba: 		return solve(d, (maxCost-minCost)/c3*3+d[1]*1+d[2]*2).val;
fa7992ffc5 2012-08-06        kinaba: 	}
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: 	mint solve(int d[3], int rem)
fa7992ffc5 2012-08-06        kinaba: 	{
fa7992ffc5 2012-08-06        kinaba: 		int n = d[0]+d[1]+d[2];
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: 		map<pair<int,int>, int> enc;
fa7992ffc5 2012-08-06        kinaba: 		for(int b=0,id=0; b<=n; ++b)
fa7992ffc5 2012-08-06        kinaba: 		for(int c=0; b+c<=n; ++c,++id)
fa7992ffc5 2012-08-06        kinaba: 			enc[make_pair(b,c)] = id;
fa7992ffc5 2012-08-06        kinaba: 		int D = enc.size();
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: 		vector< vector<mint> > M(D+1, vector<mint>(D+1));
fa7992ffc5 2012-08-06        kinaba: 		for(int b=0; b<=n; ++b)
fa7992ffc5 2012-08-06        kinaba: 		for(int c=0; b+c<=n; ++c)
fa7992ffc5 2012-08-06        kinaba: 		{
fa7992ffc5 2012-08-06        kinaba: 			int a = n-b-c;
fa7992ffc5 2012-08-06        kinaba: 			if(a) {
fa7992ffc5 2012-08-06        kinaba: 				M[enc[make_pair(b,c+1)]][enc[make_pair(b,c)]] = a;
fa7992ffc5 2012-08-06        kinaba: 			}
fa7992ffc5 2012-08-06        kinaba: 			if(b) {
fa7992ffc5 2012-08-06        kinaba: 				M[enc[make_pair(b-1,c)]][enc[make_pair(b,c)]] = b;
fa7992ffc5 2012-08-06        kinaba: 				if(b-1==0 && c==0)
fa7992ffc5 2012-08-06        kinaba: 					M.back()[enc[make_pair(b,c)]] = b;
fa7992ffc5 2012-08-06        kinaba: 			}
fa7992ffc5 2012-08-06        kinaba: 			if(c) {
fa7992ffc5 2012-08-06        kinaba: 				M[enc[make_pair(b+1,c-1)]][enc[make_pair(b,c)]] = c;
fa7992ffc5 2012-08-06        kinaba: 			}
fa7992ffc5 2012-08-06        kinaba: 		}
fa7992ffc5 2012-08-06        kinaba: 		M.back().back() = 1;
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: 		vector<mint> V(D+1);
fa7992ffc5 2012-08-06        kinaba: 		V[enc[make_pair(d[1],d[2])]] = 1;
fa7992ffc5 2012-08-06        kinaba: 		V.back() = V[0];
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: 		return MATMUL(MATPOW(M, rem), V).back();
fa7992ffc5 2012-08-06        kinaba: 	}
fa7992ffc5 2012-08-06        kinaba: };
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: // BEGIN CUT HERE
fa7992ffc5 2012-08-06        kinaba: #include <ctime>
fa7992ffc5 2012-08-06        kinaba: double start_time; string timer()
fa7992ffc5 2012-08-06        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
fa7992ffc5 2012-08-06        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
fa7992ffc5 2012-08-06        kinaba:  { os << "{ ";
fa7992ffc5 2012-08-06        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
fa7992ffc5 2012-08-06        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
fa7992ffc5 2012-08-06        kinaba: void verify_case(const int& Expected, const int& Received) {
fa7992ffc5 2012-08-06        kinaba:  bool ok = (Expected == Received);
fa7992ffc5 2012-08-06        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
fa7992ffc5 2012-08-06        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
fa7992ffc5 2012-08-06        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
fa7992ffc5 2012-08-06        kinaba: #define END	 verify_case(_, ConversionMachine().countAll(word1, word2, costs, maxCost));}
fa7992ffc5 2012-08-06        kinaba: int main(){
fa7992ffc5 2012-08-06        kinaba: 
fa7992ffc5 2012-08-06        kinaba: CASE(0)
fa7992ffc5 2012-08-06        kinaba: 	string word1 = "a";
fa7992ffc5 2012-08-06        kinaba: 	string word2 = "b";
fa7992ffc5 2012-08-06        kinaba: 	int costs_[] = {100,2,3};
fa7992ffc5 2012-08-06        kinaba: 	  vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
fa7992ffc5 2012-08-06        kinaba: 	int maxCost = 205;
fa7992ffc5 2012-08-06        kinaba: 	int _ = 2;
fa7992ffc5 2012-08-06        kinaba: END
fa7992ffc5 2012-08-06        kinaba: CASE(1)
fa7992ffc5 2012-08-06        kinaba: 	string word1 = "abcba";
fa7992ffc5 2012-08-06        kinaba: 	string word2 = "abcba";
fa7992ffc5 2012-08-06        kinaba: 	int costs_[] = {67,23,43};
fa7992ffc5 2012-08-06        kinaba: 	  vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
fa7992ffc5 2012-08-06        kinaba: 	int maxCost = 0;
fa7992ffc5 2012-08-06        kinaba: 	int _ = 1;
fa7992ffc5 2012-08-06        kinaba: END
fa7992ffc5 2012-08-06        kinaba: CASE(2)
fa7992ffc5 2012-08-06        kinaba: 	string word1 = "cccccccc";
fa7992ffc5 2012-08-06        kinaba: 	string word2 = "aaaaaaaa";
fa7992ffc5 2012-08-06        kinaba: 	int costs_[] = {10000000,1,1};
fa7992ffc5 2012-08-06        kinaba: 	  vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
fa7992ffc5 2012-08-06        kinaba: 	int maxCost = 100;
fa7992ffc5 2012-08-06        kinaba: 	int _ = 40320;
fa7992ffc5 2012-08-06        kinaba: END
fa7992ffc5 2012-08-06        kinaba: CASE(3)
fa7992ffc5 2012-08-06        kinaba: 	string word1 = "aa";
fa7992ffc5 2012-08-06        kinaba: 	string word2 = "cc";
fa7992ffc5 2012-08-06        kinaba: 	int costs_[] = {1,10,100};
fa7992ffc5 2012-08-06        kinaba: 	  vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
fa7992ffc5 2012-08-06        kinaba: 	int maxCost = 1787;
fa7992ffc5 2012-08-06        kinaba: 	int _ = 123611681;
fa7992ffc5 2012-08-06        kinaba: END
fa7992ffc5 2012-08-06        kinaba: /*
fa7992ffc5 2012-08-06        kinaba: CASE(4)
fa7992ffc5 2012-08-06        kinaba: 	string word1 = ;
fa7992ffc5 2012-08-06        kinaba: 	string word2 = ;
fa7992ffc5 2012-08-06        kinaba: 	int costs_[] = ;
fa7992ffc5 2012-08-06        kinaba: 	  vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
fa7992ffc5 2012-08-06        kinaba: 	int maxCost = ;
fa7992ffc5 2012-08-06        kinaba: 	int _ = ;
fa7992ffc5 2012-08-06        kinaba: END
fa7992ffc5 2012-08-06        kinaba: CASE(5)
fa7992ffc5 2012-08-06        kinaba: 	string word1 = ;
fa7992ffc5 2012-08-06        kinaba: 	string word2 = ;
fa7992ffc5 2012-08-06        kinaba: 	int costs_[] = ;
fa7992ffc5 2012-08-06        kinaba: 	  vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
fa7992ffc5 2012-08-06        kinaba: 	int maxCost = ;
fa7992ffc5 2012-08-06        kinaba: 	int _ = ;
fa7992ffc5 2012-08-06        kinaba: END
fa7992ffc5 2012-08-06        kinaba: */
fa7992ffc5 2012-08-06        kinaba: }
fa7992ffc5 2012-08-06        kinaba: // END CUT HERE