Kortit II

#include <iostream>
#include <vector>

using namespace std;

const int MOD = 1e9 + 7;

// Function to compute factorial modulo MOD
vector<long long> compute_factorials(int max_n)
{
    vector<long long> fact(max_n + 1);
    fact[0] = 1;
    for (int i = 1; i <= max_n; ++i)
    {
        fact[i] = (fact[i - 1] * i) % MOD;
    }
    return fact;
}

// Function to compute modular inverse using Fermat's Little Theorem
long long mod_inverse(long long a)
{
    long long res = 1, exp = MOD - 2; // a^(MOD-2) % MOD
    while (exp > 0)
    {
        if (exp % 2 == 1)
        {
            res = (res * a) % MOD;
        }
        a = (a * a) % MOD;
        exp /= 2;
    }
    return res;
}

// Function to compute nCr % MOD
long long nCr(int n, int r, const vector<long long> &fact)
{
    if (r > n || r < 0)
        return 0;
    return (fact[n] * mod_inverse(fact[r]) % MOD * mod_inverse(fact[n - r]) % MOD) % MOD;
}

// Main function to count valid game configurations
long long count_games(int n, int target_a, int target_b, const vector<long long> &fact)
{
    if (target_a + target_b > n)
        return 0; // Not enough cards for wins

    // Calculate the number of ways
    long long total_ways = 0;

    // Iterate over all possible distributions of ties
    for (int ties = 0; ties <= n - target_a - target_b; ++ties)
    {
        // Calculate combinations for player A's wins and player B's wins
        long long ways_a = nCr(n, target_a, fact);            // Choose cards for player A's wins
        long long ways_b = nCr(n - target_a, target_b, fact); // Choose remaining cards for player B's wins

        // Multiply by the arrangements of ties
        total_ways = (total_ways + ways_a * ways_b % MOD * fact[ties] % MOD) % MOD;
    }

    return total_ways;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int t;
    cin >> t;

    const int MAX_N = 2000;
    vector<long long> fact = compute_factorials(MAX_N);

    while (t--)
    {
        int n, a, b;
        cin >> n >> a >> b;

        long long result = count_games(n, a, b, fact);
        cout << result << '\n';
    }

    return 0;
}

Test 1

Group: 1, 2, 3, 4, 5

Verdict: WRONG ANSWER

Test 2

Group: 2, 3, 4, 5

Verdict: WRONG ANSWER

Test 3

Group: 3, 4, 5

Verdict: WRONG ANSWER

Test 4

Group: 4, 5

Verdict: WRONG ANSWER

Test 5

Group: 5

Verdict: WRONG ANSWER

Test 6

Group: 5

Verdict: WRONG ANSWER