#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 int MODVAL = 1000000009;
class YetAnotherIncredibleMachine { public:
int countWays(vector <int> platformMount, vector <int> platformLength, vector <int> balls)
{
LL total = 1;
for(int p=0; p<platformLength.size(); ++p)
{
vector< pair<int,int> > q;
int len = platformLength[p];
int pos = platformMount[p];
q.push_back( make_pair(pos-len, pos) );
for(int i=0; i<balls.size(); ++i)
avoid( balls[i], q, len );
int cnt = 0;
for(int i=0; i<q.size(); ++i)
cnt += q[i].second - q[i].first + 1;
total = total * cnt % MODVAL;
}
return int(total);
}
void avoid(int x, vector< pair<int,int> >& q, int len)
{
vector< pair<int,int> > q2;
for(int i=0; i<q.size(); ++i)
if( q[i].second+len < x || x < q[i].first )
q2.push_back( q[i] );
else {
int L = q[i].first;
int R = q[i].second;
if( L<=x-len-1 )
q2.push_back( make_pair(L, x-len-1) );
if( x+1<=R )
q2.push_back( make_pair(x+1, R) );
}
q.swap(q2);
}
};
// 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(_, YetAnotherIncredibleMachine().countWays(platformMount, platformLength, balls));}
int main(){
CASE(0)
int platformMount_[] = {7};
vector <int> platformMount(platformMount_, platformMount_+sizeof(platformMount_)/sizeof(*platformMount_));
int platformLength_[] = {10};
vector <int> platformLength(platformLength_, platformLength_+sizeof(platformLength_)/sizeof(*platformLength_));
int balls_[] = {3,4};
vector <int> balls(balls_, balls_+sizeof(balls_)/sizeof(*balls_));
int _ = 3;
END
CASE(1)
int platformMount_[] = {1,4};
vector <int> platformMount(platformMount_, platformMount_+sizeof(platformMount_)/sizeof(*platformMount_));
int platformLength_[] = {3,3};
vector <int> platformLength(platformLength_, platformLength_+sizeof(platformLength_)/sizeof(*platformLength_));
int balls_[] = {2,7};
vector <int> balls(balls_, balls_+sizeof(balls_)/sizeof(*balls_));
int _ = 1;
END
CASE(2)
int platformMount_[] = {4,4,4};
vector <int> platformMount(platformMount_, platformMount_+sizeof(platformMount_)/sizeof(*platformMount_));
int platformLength_[] = {10,9,8};
vector <int> platformLength(platformLength_, platformLength_+sizeof(platformLength_)/sizeof(*platformLength_));
int balls_[] = {1,100};
vector <int> balls(balls_, balls_+sizeof(balls_)/sizeof(*balls_));
int _ = 27;
END
CASE(3)
int platformMount_[] = {0};
vector <int> platformMount(platformMount_, platformMount_+sizeof(platformMount_)/sizeof(*platformMount_));
int platformLength_[] = {1};
vector <int> platformLength(platformLength_, platformLength_+sizeof(platformLength_)/sizeof(*platformLength_));
int balls_[] = {0};
vector <int> balls(balls_, balls_+sizeof(balls_)/sizeof(*balls_));
int _ = 0;
END
CASE(4)
int platformMount_[] = {100, -4215, 251};
vector <int> platformMount(platformMount_, platformMount_+sizeof(platformMount_)/sizeof(*platformMount_));
int platformLength_[] = {400, 10000, 2121};
vector <int> platformLength(platformLength_, platformLength_+sizeof(platformLength_)/sizeof(*platformLength_));
int balls_[] = {5000, 2270, 8512, 6122};
vector <int> balls(balls_, balls_+sizeof(balls_)/sizeof(*balls_));
int _ = 250379170;
END
/*
CASE(5)
int platformMount_[] = ;
vector <int> platformMount(platformMount_, platformMount_+sizeof(platformMount_)/sizeof(*platformMount_));
int platformLength_[] = ;
vector <int> platformLength(platformLength_, platformLength_+sizeof(platformLength_)/sizeof(*platformLength_));
int balls_[] = ;
vector <int> balls(balls_, balls_+sizeof(balls_)/sizeof(*balls_));
int _ = ;
END
CASE(6)
int platformMount_[] = ;
vector <int> platformMount(platformMount_, platformMount_+sizeof(platformMount_)/sizeof(*platformMount_));
int platformLength_[] = ;
vector <int> platformLength(platformLength_, platformLength_+sizeof(platformLength_)/sizeof(*platformLength_));
int balls_[] = ;
vector <int> balls(balls_, balls_+sizeof(balls_)/sizeof(*balls_));
int _ = ;
END
*/
}
// END CUT HERE