This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*
This code belongs to Aadit Ambadkar
Date: 2021-12-25 16:34:50
Problem: tower
*/
#include <bits/stdc++.h>
using namespace::std;
typedef long long ll;
#define F0R(i, n) for (int i = 0; i < n; i++)
#define R0F(i, n) for (int i = n-1; i >= 0; i--)
#define FOR(i, a, n) for (int i = a; i < n; i++)
#define pb push_back
#define fastio ios::sync_with_stdio(0); cin.tie(0)
#define MOD 1000000009
#define FF first
#define SS second
int main() {
fastio;
int n, d; cin >> n >> d;
vector<int> v;
F0R(i, n) {
int x; cin >> x;
v.pb(x);
}
sort(v.begin(), v.end());
vector<ll> dp(n, 0);
dp[0]=1;
int p = 0;
FOR(i, 1, n) {
while (v[i]-v[p]>d) p++;
dp[i]=dp[i-1]*(i-p+1);
dp[i]%=MOD;
}
cout << dp[n-1] << "\n";
}
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