Kortit II

#include <iostream>

using namespace std;

typedef long long ll;

const ll m = 1000000007;

const ll n = 3000;

ll t[n][n+1];
ll f[n+1];
ll p[n+1][n+1];

ll madd(ll a, ll b)
{
  return ((a % m) + (b % m)) % m;
}

ll mmul(ll a, ll b)
{
  return ((a % m) * (b % m)) % m;
}

void init()
{
  f[0] = 1;
  for (ll i = 1; i < n+1; i++)
  {
    f[i] = mmul(i, f[i-1]);
  }

  t[0][0] = 1;
  
  for (ll i = 2; i < n+1; i++)
  {
    t[1][i] = 1;
  }

  for (ll i = 3; i < n+1; i++)
  {
    t[i-1][i] = 1;
  }

  for (ll j = 4; j < n+1; j++)
  {
    for (ll i = 2; i < j-1; i++)
    {
      //t[i][j] = i * t[i][j-1] + (j-i) * t[i-1][j-1] + (j-1) * t[i-1][j-2];
      t[i][j] = (mmul(i, t[i][j-1]) + mmul(j-i, t[i-1][j-1]) + mmul(j-1, t[i-1][j-2])) % m;
    }
  }

  p[0][0] = 1; // C(0, 0) = 1

  for (int i = 1; i < n; i++) {
    p[i][0] = 1; // C(i, 0) = 1
    for (int j = 1; j <= i; j++) {
      p[i][j] = madd(p[i - 1][j - 1], p[i - 1][j]);
    }
  }
}

long long ncr(int n, int r) {
  return p[n][r];
}

void print()
{
  for (ll i = 0; i < n+1; i++)
  {
    cout << f[i] << " ";
  }
  cout << endl << endl;

  for (ll j = 0; j < n+1; j++)
  {
    for (ll i = 0; i < n; i++)
    {
      cout << t[i][j] << " ";
    }
    cout << endl;
  }
}

int main()
{
  init();

  int tests, n, a, b;

  cin >> tests;

  for (int i = 0; i < tests; i++)
  {
    cin >> n >> a >> b;

    if (a + b > n)
    {
      cout << 0 << endl;
      continue;
    }

    int numberOfDraws = n - a - b;

    if (numberOfDraws < n && (a == n - numberOfDraws || b == n - numberOfDraws))
    {
      cout << 0 << endl;
      continue;
    }

    ll c = a + b;

    ll v = mmul(mmul(t[a][c], ncr(n, n-c)), f[n]);

    cout << v << endl;
  }
}

Test 1

Group: 1, 2, 3, 4, 5

Verdict: ACCEPTED

Test 2

Group: 2, 3, 4, 5

Verdict: ACCEPTED

Test 3

Group: 3, 4, 5

Verdict: ACCEPTED

Test 4

Group: 4, 5

Verdict: ACCEPTED

Test 5

Group: 5

Verdict: ACCEPTED

Test 6

Group: 5

Verdict: ACCEPTED