This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define int long long
using namespace std;
namespace std {
template <typename T> ostream &operator<<(ostream &out, const vector<T> &vec) {
out << "[";
for (int i = 0; i < (int)vec.size(); ++i) {
out << vec[i];
if (i + 1 < (int)vec.size())
out << ", ";
}
return out << "]";
}
} // namespace std
void dbg_out() { cout << endl; }
template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) {
cout << ' ' << H;
dbg_out(T...);
}
#ifdef DEBUG
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif
const int MOD = 1e9 + 9;
signed main(void) {
ios_base::sync_with_stdio(false);
cin.tie(0);
int N, d;
cin >> N >> d;
vector<int> a(N);
for (int &x : a)
cin >> x;
sort(a.begin(), a.end());
dbg(a);
int sol = 1;
for (int i = 1; i < N; ++i) {
int from = lower_bound(a.begin(), a.end(), a[i] - d) - a.begin();
dbg(i, from);
sol = sol * (i - from + 1) % MOD;
}
cout << sol << endl;
}
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