如果我使用递归运行C++程序，则显示大于12的数的阶乘的值错误

#include <iostream>

unsigned long long factorial(unsigned int n) {
    if (n == 0 || n == 1) {
        return 1;
    } else {
        return n * factorial(n - 1);
    }
}

int main() {
    unsigned int num;
    std::cout << "Enter a number: ";
    std::cin >> num;

    if (num > 12) {
        std::cout << "Factorial of " << num << " is too large to display correctly using unsigned long long." << std::endl;
    } else {
        std::cout << "Factorial of " << num << " is " << factorial(num) << std::endl;
    }

    return 0;
}

#include <iostream>

unsigned long long factorial(unsigned int n) {
    unsigned long long result = 1;
    for (unsigned int i = 1; i <= n; ++i) {
        result *= i;
    }
    return result;
}

int main() {
    unsigned int num;
    std::cout << "Enter a number: ";
    std::cin >> num;

    if (num > 12) {
        std::cout << "Factorial of " << num << " is too large to display correctly using unsigned long long." << std::endl;
    } else {
        std::cout << "Factorial of " << num << " is " << factorial(num) << std::endl;
    }

    return 0;
}