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 ll long long
#define ld long double
#define sp ' '
#define en '\n'
#define smin(a, b) a = min(a, b)
#define smax(a, b) a = max(a, b)
using namespace std;
const int N = 1e5 + 2;
const int inf = 1e9;
const int mod = 1e9 + 9;
ll Mul(ll a, ll b) {
ll c = a; c *= b; c %= mod;
return c;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int n, d;
cin >> n >> d;
vector<int> a(n);
for (int i = 0; i < n; i++) cin >> a[i];
sort(a.begin(), a.end());
ll ans = 1;
int j = 0;
for (int i = 1; i < n; i++) {
while (j < i && a[j] + d < a[i]) j++;
ans = Mul(ans, i - j + 1);
}
cout << ans << en;
return 0;
}
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