#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
#include <cstring>
using namespace std;
typedef long long LL;
static const int MODVAL = 1000000007;
int ADD(int x, int y) { return (x+y)%MODVAL; }
int SUB(int x, int y) { return (x-y+MODVAL)%MODVAL; }
class Unicorn {
public:
int countWays(int R, int C, int L, int seed, string word)
{
// input...
char B[300][300];
{
int x = seed;
int d = (65535 / L)+1;
for (int r=0; r<R; r++)
for (int c=0; c<C; c++) {
x = (x * 25173 + 13849) % 65536;
B[r][c] = (65+(x / d));
}
}
// solve
vector<int> cnt(C*R);
for(int r=0; r<R; ++r)
for(int c=0; c<C; ++c)
if( B[r][c] == word[0] )
cnt[r*C+c] = 1;
for(int i=1; i<word.size(); ++i)
{
int total_cnt = 0;
vector<int> c_cnt(C);
vector<int> r_cnt(R);
for(int r=0; r<R; ++r)
for(int c=0; c<C; ++c)
r_cnt[r] = ADD( r_cnt[r], cnt[r*C+c]),
c_cnt[c] = ADD( c_cnt[c], cnt[r*C+c]),
total_cnt = ADD(total_cnt, cnt[r*C+c]);
vector<int> cnt2(C*R);
for(int r=0; r<R; ++r)
for(int c=0; c<C; ++c)
if( B[r][c] == word[i] )
{
int x = total_cnt;
for(int rr=r-1; rr<=r+1; ++rr) if(0<=rr && rr<R)
x = SUB(x, r_cnt[rr]);
for(int cc=c-1; cc<=c+1; ++cc) if(0<=cc && cc<C)
x = SUB(x, c_cnt[cc]);
for(int rr=r-1; rr<=r+1; ++rr) if(0<=rr && rr<R)
for(int cc=c-1; cc<=c+1; ++cc) if(0<=cc && cc<C)
x = ADD(x, cnt[rr*C+cc]);
for(int rr=r-2; rr<=r+2; rr+=4) if(0<=rr && rr<R)
for(int cc=c-2; cc<=c+2; cc+=4) if(0<=cc && cc<C)
x = SUB(x, cnt[rr*C+cc]);
cnt2[r*C+c] = x;
}
cnt.swap(cnt2);
}
int live = 0;
for(int r=0; r<R; ++r)
for(int c=0; c<C; ++c)
live = ADD(live, cnt[r*C+c]);
return live;
}
};
// 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> string print_array(const vector<T> &V) { ostringstream os; os << "{ "; for (typename vector<T>::const_iterator iter = V.begin(); iter != V.end(); ++iter) os << '\"' << *iter << "\","; os << " }"; return os.str(); }
int verify_case(const int &Expected, const int &Received) { if (Expected == Received) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl; cerr << "\tExpected: \"" << Expected << '\"' << endl; cerr << "\tReceived: \"" << Received << '\"' << endl; } return 0;}
template<int N> struct Case_ { Case_(){start_time=clock();} };
char Test_(...);
int Test_(Case_<0>) {
int R = 3;
int C = 4;
int L = 2;
int seed = 47;
string word = "AB";
int RetVal = 2;
return verify_case(RetVal, Unicorn().countWays(R, C, L, seed, word)); }
int Test_(Case_<1>) {
int R = 5;
int C = 5;
int L = 2;
int seed = 47;
string word = "CD";
int RetVal = 0;
return verify_case(RetVal, Unicorn().countWays(R, C, L, seed, word)); }
int Test_(Case_<2>) {
int R = 4;
int C = 4;
int L = 1;
int seed = 42;
string word = "AA";
int RetVal = 20;
return verify_case(RetVal, Unicorn().countWays(R, C, L, seed, word)); }
int Test_(Case_<3>) {
int R = 4;
int C = 4;
int L = 1;
int seed = 42;
string word = "AAAAA";
int RetVal = 172;
return verify_case(RetVal, Unicorn().countWays(R, C, L, seed, word)); }
int Test_(Case_<4>) {
int R = 1;
int C = 1;
int L = 5;
int seed = 54321;
string word = "ABCDE";
int RetVal = 0;
return verify_case(RetVal, Unicorn().countWays(R, C, L, seed, word)); }
int Test_(Case_<5>) {
int R = 8;
int C = 8;
int L = 26;
int seed = 226;
string word = "TOPCODER";
int RetVal = 1;
return verify_case(RetVal, Unicorn().countWays(R, C, L, seed, word)); }
int Test_(Case_<6>) {
int R = 20;
int C = 20;
int L = 2;
int seed = 47;
string word = "AAAAA";
int RetVal = 373977054;
return verify_case(RetVal, Unicorn().countWays(R, C, L, seed, word)); }
template<int N> void Run_() { cerr << "Test Case #" << N << "..." << flush; Test_(Case_<N>()); Run_<sizeof(Test_(Case_<N+1>()))==1 ? -1 : N+1>(); }
template<> void Run_<-1>() {}
int main() { Run_<0>(); }
// END CUT HERE