#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 = 1000000007;
struct mint
{
int val;
mint():val(0){}
mint(int x):val(x%MODVAL) {}
mint(size_t 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 = LL(x.val)*y.val; }
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 ConversionMachine { public:
int countAll(string word1, string word2, vector <int> costs, int maxCost)
{
int d[3] = {};
LL minCost = 0;
for(int i=0; i<word1.size(); ++i) {
int dd=0;
while( word1[i] != word2[i] ) {
dd += 1;
minCost += costs[word1[i]-'a'];
word1[i] = (word1[i]+1-'a')%3 + 'a';
}
d[dd] += 1;
}
if( minCost > maxCost )
return 0;
LL c3 = accumulate(costs.begin(), costs.end(), 0LL);
return solve(d, (maxCost-minCost)/c3*3+d[1]*1+d[2]*2).val;
}
mint solve(int d[3], int rem)
{
int n = d[0]+d[1]+d[2];
map<pair<int,int>, int> enc;
for(int b=0,id=0; b<=n; ++b)
for(int c=0; b+c<=n; ++c,++id)
enc[make_pair(b,c)] = id;
int D = enc.size();
vector< vector<mint> > M(D+1, vector<mint>(D+1));
for(int b=0; b<=n; ++b)
for(int c=0; b+c<=n; ++c)
{
int a = n-b-c;
if(a) {
M[enc[make_pair(b,c+1)]][enc[make_pair(b,c)]] = a;
}
if(b) {
M[enc[make_pair(b-1,c)]][enc[make_pair(b,c)]] = b;
if(b-1==0 && c==0)
M.back()[enc[make_pair(b,c)]] = b;
}
if(c) {
M[enc[make_pair(b+1,c-1)]][enc[make_pair(b,c)]] = c;
}
}
M.back().back() = 1;
vector<mint> V(D+1);
V[enc[make_pair(d[1],d[2])]] = 1;
V.back() = V[0];
return MATMUL(MATPOW(M, rem), V).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(_, ConversionMachine().countAll(word1, word2, costs, maxCost));}
int main(){
CASE(0)
string word1 = "a";
string word2 = "b";
int costs_[] = {100,2,3};
vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
int maxCost = 205;
int _ = 2;
END
CASE(1)
string word1 = "abcba";
string word2 = "abcba";
int costs_[] = {67,23,43};
vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
int maxCost = 0;
int _ = 1;
END
CASE(2)
string word1 = "cccccccc";
string word2 = "aaaaaaaa";
int costs_[] = {10000000,1,1};
vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
int maxCost = 100;
int _ = 40320;
END
CASE(3)
string word1 = "aa";
string word2 = "cc";
int costs_[] = {1,10,100};
vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
int maxCost = 1787;
int _ = 123611681;
END
/*
CASE(4)
string word1 = ;
string word2 = ;
int costs_[] = ;
vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
int maxCost = ;
int _ = ;
END
CASE(5)
string word1 = ;
string word2 = ;
int costs_[] = ;
vector <int> costs(costs_, costs_+sizeof(costs_)/sizeof(*costs_));
int maxCost = ;
int _ = ;
END
*/
}
// END CUT HERE