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 <iostream>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#define ll signed long long
using namespace std;
const ll MOD = (ll)10e9 + 9;
bool cmpr(ll a, ll b)
{
return a > b;
}
int main()
{
cin.tie(0);
cout.tie(0);
ios_base::sync_with_stdio(0);
//freopen("tower.in", "r", stdin);
ll N;
ll D;
cin >> N >> D;
vector<ll> blocks(N, 0);
for (ll i = 0; i < N; i++)
{
cin >> blocks[i];
}
sort(blocks.begin(), blocks.end(), cmpr);
vector<ll> possible(N, 0);
ll sum = 1;
ll j = 0;
for (ll i = 0; i < N; i++)
{
j = max(j, i);
sum = 1;
while (j < N - 1 && blocks[i] - blocks[j + 1] <= D)
{
j++;
sum *= (j - i + 1) % MOD;
sum %= MOD;
}
possible[i] = sum;
}
ll sol = possible[0];
for (ll i = 1; i < N; i++)
{
if (blocks[i - 1] - blocks[i] <= D)
{
if (possible[i] != 1)
{
sol += possible[i];
}
}
else
{
sol *= possible[i];
}
sol %= MOD;
}
cout << sol;
}
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