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>
using namespace std;
using ll = long long;
const int MOD = 1e9+9;
ll factorial(ll n){
if(n==0) return 1;
return n*factorial(n-1);
}
int main() {
ll n, d;
cin>>n>>d;
ll arr[n];
for(ll i=0; i<n; i++){
cin>>arr[i];
}
sort(arr, arr+n);
map<ll, ll> m; // value, number of values
ll l = 0, r = 0;
for(; l<n; l++){
if(arr[l]+d<arr[r]){
l = r;
}
while(arr[l]+d>=arr[r] && r<n){
m[l]=r-l+1;
r++;
}
}
ll ans = 1;
for(auto u: m){
ans*=factorial(u.second);
}
cout<<(ans%MOD);
}
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