This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*
*
* ^v^
*
*/
#include <iostream>
#include <numeric>
#include <set>
#include <iomanip>
#include <chrono>
#include <queue>
#include <string>
#include <vector>
#include <functional>
#include <map>
#include <bitset>
#include <algorithm>
#include <array>
#include <random>
using namespace std;
using ll = long long int;
using ld = long double;
#define iamtefu ios_base::sync_with_stdio(false); cin.tie(0);
#define fl(i,a,n) for (ll i{a}; i<n; i++)
#define fr(x,s) for(auto x:s)
#define rfl(i,a,n) for (ll i{n-1}; i>=a; i--)
#define ty int _; for(cin>>_; _--;)
#define print(a) for(auto ele:a){cout<<ele<<" ";}cout<<'\n';
#define all(x) x.begin(), x.end()
template <typename L, typename R>
inline bool chmax(L &a, R b){if (a<b){a=b;return 1;}return 0;}
template <typename L, typename R>
inline bool chmin(L &a, R b){if (a>b){a=b;return 1;}return 0;}
template <typename L, typename R>
ostream& operator<<(ostream &fout, const pair<L, R> &p){
fout<<"{"<<p.first<<","<<p.second<<"}";
return fout;
}
template <typename L, typename R, typename U>
ostream& operator<<(ostream &fout, const tuple<L, R, U> &p){
auto &[l, r, u] = p;
fout<<"{"<<l<<","<<r<<","<<u<<"}";
return fout;
}
template <typename T>
ostream& operator<<(ostream &fout, const vector <T> &v){
for (auto &x:v){
fout<<x<<" ";
}
fout<<"\n";
return fout;
}
template <typename T>
ostream& operator<<(ostream &fout, const set <T> &st){
for (auto &x:st){
fout<<x<<" ";
}
fout<<"\n";
return fout;
}
template <typename T>
ostream& operator<<(ostream &fout, const multiset <T> &st){
for (auto &x:st){
fout<<x<<" ";
}
fout<<"\n";
return fout;
}
template <typename K, typename V>
ostream& operator<<(ostream &fout, const map<K, V> &mp){
fout<<"[";
for (auto &[x,y]:mp){
fout<<x<<":"<<y<<" ";
}
fout<<"]\n";
return fout;
}
ll gcd(ll a, ll b){
if (b==0){
return a;
}
return gcd(b, a%b);
}
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll pw(ll a, ll b, ll m){
ll res=1;
a%=m;
while (b){
if (b&1){
res=(res*a)%m;
}
a=(a*a)%m;
b/=2;
}
return res;
}
const ll mod = 1e9+9;
void scn(){
// not necessarily distinct
// right down
ll n, k; cin>>n>>k;
vector <ll> a(n);
fl(i,0,n){
cin>>a[i];
}
sort(all(a));
ll l = 0;
vector <ll> ans(n+1, 1);
fl(j,0,n){
while (l<j && a[j]-a[l]>k){
l++;
}
ans[j+1] = (ans[j]*(j-l+1))%mod;
}
cout<<ans.back()<<'\n';
}
int main(){
iamtefu;
#if defined(airths)
auto t1=chrono::high_resolution_clock::now();
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
// ty
{
scn();
}
#if defined(airths)
auto t2=chrono::high_resolution_clock::now();
ld ti=chrono::duration_cast<chrono::nanoseconds>(t2-t1).count();
ti*=1e-6;
cerr<<"Time: "<<setprecision(12)<<ti;
cerr<<"ms\n";
#endif
return 0;
}
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