Kortit II

#include <iostream>
#include <vector>
#include <algorithm>

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)
{
    long long total_ways = 0;

    // Iterate over all possible ways to distribute wins
    for (int wins_a = target_a; wins_a <= n; ++wins_a)
    {
        int wins_b = n - wins_a; // Remaining wins go to player B

        if (wins_b < target_b)
            continue; // Not enough wins for player B

        // Calculate the number of ways to choose which cards win for player A and B
        long long ways_a = nCr(n, wins_a, fact);
        long long ways_b = nCr(n - wins_a, wins_b, fact); // Choose remaining for player B

        total_ways = (total_ways + ways_a * ways_b % 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