#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 unsigned MODVAL = 1000000009;
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>
struct DP4x
{
int N1, N2, N3, N4;
vector<T> data;
DP4x(int, int N2, int N3, int N4, const T& t = T())
: N1(2), N2(N2), N3(N3), N4(N4), data(N1*N2*N3*N4, t) { assert(data.size()*sizeof(T)<(1<<26)); }
T& operator()(int i1, int i2, int i3, int i4)
{ i1&=1; return data[ (((i1*N2)+i2)*N3+i3)*N4+i4 ]; }
void swap(DP4x& rhs)
{ data.swap(rhs.data); }
};
class TheExperiment { public:
int countPlacements(vector <string> intensity, int M, int L, int A, int B)
{
string S = accumulate(intensity.begin(), intensity.end(), string());
int N = S.size();
vector<int> range_L, range_R; // [L,R)
{
vector<int> PS(N+1, 0);
for(int i=0; i<N; ++i)
PS[i+1] = PS[i] + (S[i]-'0');
for(int i=0; i<N; ++i)
{
int LL = PS[i]+A;
int RR = PS[i]+B+1;
range_L.push_back(lower_bound(PS.begin(), PS.end(), LL) - PS.begin());
range_R.push_back(lower_bound(PS.begin(), PS.end(), RR) - PS.begin());
//cerr<<i<<" ["<<range_L.back()<<"-"<<range_R.back()<<")"<<" "<<LL<<","<<RR<<endl;
}
}
DP4x<mint> dp(M+1, N+1, M, 2);
dp(0, 0, 0, 0) = 1;
for(int i=0; i<M; ++i)
{
// Clear
for(int x=0; x<=N; ++x)
for(int rank=0; rank<M; ++rank) {
for(int hami=0; hami<2; ++hami) {
if(dp(i,x,rank,hami).val)
cerr<<i<<" "<<x<<" "<<rank<<" "<<hami<<" : "<< dp(i,x,rank,hami).val<<endl;
dp(i+1, x, rank, hami) = 0;
}
// DP
for(int x=0; x<N; ++x)
for(int rank=0; rank<=i; ++rank)
for(int hami=0; hami<2; ++hami)
{
mint v = dp(i,x,rank,hami);
if(v.val != 0)
for(int y=range_L[x]; y<range_R[x]; ++y)
{
if(y-x < L) {
if(hami) {
for(int r=0; r<=rank; ++r)
dp(i+1, y, a) += v;
} else {
}
} else if(y-x == L) {
if(hami)
dp(i+1, y, i, 0) += v * (rank+1);
else
dp(i+1, y, i, 0) += v * (rank+1);
} else {
break;
}
}
}
}
mint acc = 0;
for(int rank=0; rank<M; ++rank)
acc += dp(M, N, rank, 0);
return acc.val;
}
};
// 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(_, TheExperiment().countPlacements(intensity, M, L, A, B));}
int main(){
CASE(0)
string intensity_[] = {"341156"};
vector <string> intensity(intensity_, intensity_+sizeof(intensity_)/sizeof(*intensity_));
int M = 3;
int L = 3;
int A = 6;
int B = 10;
int _ = 2;
END
CASE(1)
string intensity_[] = {"999112999"};
vector <string> intensity(intensity_, intensity_+sizeof(intensity_)/sizeof(*intensity_));
int M = 2;
int L = 4;
int A = 21;
int B = 30;
int _ = 2;
END
CASE(2)
string intensity_[] = {"111"};
vector <string> intensity(intensity_, intensity_+sizeof(intensity_)/sizeof(*intensity_));
int M = 2;
int L = 2;
int A = 2;
int B = 3;
int _ = 0;
END
CASE(3)
string intensity_[] = {"59059", "110", "1132230231"};
vector <string> intensity(intensity_, intensity_+sizeof(intensity_)/sizeof(*intensity_));
int M = 1;
int L = 5;
int A = 10;
int B = 20;
int _ = 6;
END
CASE(4)
string intensity_[] = {"111111111111111111111111", "111111111111111111111111111", "11111111111111111111111"};
vector <string> intensity(intensity_, intensity_+sizeof(intensity_)/sizeof(*intensity_));
int M = 12;
int L = 8;
int A = 4;
int B = 2700;
int _ = 418629948;
END
/*
CASE(5)
string intensity_[] = ;
vector <string> intensity(intensity_, intensity_+sizeof(intensity_)/sizeof(*intensity_));
int M = ;
int L = ;
int A = ;
int B = ;
int _ = ;
END
CASE(6)
string intensity_[] = ;
vector <string> intensity(intensity_, intensity_+sizeof(intensity_)/sizeof(*intensity_));
int M = ;
int L = ;
int A = ;
int B = ;
int _ = ;
END
*/
}
// END CUT HERE