#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>
#include <cstring>
using namespace std;
typedef long long LL;
typedef complex<double> CMP;
static const LL MODVAL = 1000000009; // must fit in 32-bits
LL ADD(LL x, LL y) { return (x+y)%MODVAL; }
LL SUB(LL x, LL y) { return (x-y+MODVAL)%MODVAL; }
LL MUL(LL x, LL y) { return (x*y)%MODVAL; }
LL POW(LL x, LL e) {
LL v = 1;
for(;e;x=MUL(x,x),e>>=1)
if(e&1)
v = MUL(v, x);
return v;
}
LL DIV(LL x, LL y) { return MUL(x, POW(y, MODVAL-2)); }
class RabbitIncreasing { public:
int getNumber(vector <int> leaving, int k)
{
if( leaving.front() <= 1 )
return 0;
int li = 0;
LL y[] = {1,0,0};
LL p[] = {1,0,0};
LL PP = (1LL << 55);
for(int i=2; i<=k; ++i)
{
LL a=y[0], b=y[1], c=y[2];
y[0]=y[2]=ADD(b,c); y[1]=a;
LL pa=p[0], pb=p[1], pc=p[2];
p[0]=p[2]=(pb+pc)%PP; p[1]=pa;
if( li<leaving.size() && i==leaving[li] ) {
++li;
y[2] = 0;
p[2] = 0;
if( p[1]&1 ) {
y[1]=DIV(SUB(y[1],1),2);
} else {
y[1]=DIV(y[1],2);
}
p[1]=p[1]/2;
PP >>= 1;
}
}
return ADD(y[0],ADD(y[1],y[2]));
}
};
// 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(_, RabbitIncreasing().getNumber(leaving, k));}
int main(){
CASE(0)
int leaving_[] = { 3 };
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 3;
int _ = 1;
END
CASE(1)
int leaving_[] = { 5, 9 };
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 10;
int _ = 6;
END
CASE(2)
int leaving_[] = { 5, 10, 15 };
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 19;
int _ = 212;
END
CASE(3)
int leaving_[] = { 2 };
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 10000000;
int _ = 0;
END
CASE(4)
int leaving_[] = { 195, 211, 227, 230, 260,
297, 346, 350, 403, 411,
428, 485, 594, 606, 876 }
;
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 1000;
int _ = 975206486;
END
CASE(5)
int leaving_[] = {2};
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 1;
int _ = 1;
END
CASE(5)
int leaving_[] = {2};
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 2;
int _ = 0;
END
CASE(5)
int leaving_[] = {1};
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 1;
int _ = 0;
END
CASE(6)
int leaving_[] = {999};
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 10000000;
int _ = 536491299;
END
CASE(7)
int leaving_[] = {
100,200,300,400,500,600,700,800,900,1000,
1100,1200,1300,1400,1500,1600,1700,1800,1900,2000,
3100,3200,3300,3400,3500,3600,3700,3800,3900,31000,
43100,43200,43300,43400,43500,43600,43700,43800,43900,431000,
999100,999200,999300,999400,999500,999600,999700,999800,999900,9991000,
};
vector <int> leaving(leaving_, leaving_+sizeof(leaving_)/sizeof(*leaving_));
int k = 10000000;
int _ = 260357174;
END
}
// END CUT HERE