1359. Count All Valid Pickup and Delivery Options.cpp

// 1359.✅ Count All Valid Pickup and Delivery Options

class Solution
{
public:
    int countOrders(int n)
    {
        long res = 1, mod = 1000000007;
        for (int i = 1; i <= n; ++i)
        {
            // calulating n!
            res *= i;
            // to avoid overflow
            res %= mod;

            // (2*i-1) are the vacant places which we can choose
            // later we have n! permutation of pickup task
            // therefore we have to multiply with n! that we calculated as res.
            res *= (2 * i - 1);

            // to avoid overflow
            res %= mod;
        }

        // to avoid overflow
        return res % mod;
    }
};