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#include <iostream>
#include <vector>

// 使用试除法找到一个数的所有质因数
std::vector<long long> primeFactors(long long n) {
    std::vector<long long> factors;

    // 循环除以2，直到n为奇数
    while (n % 2 == 0) {
        factors.push_back(2);
        n = n / 2;
    }

    // 从3开始尝试除以奇数
    for (int i = 3; i * i <= n; i = i + 2) {
        while (n % i == 0) {
            factors.push_back(i);
            n = n / i;
        }
    }

    // 如果n是一个大于2的质数，则将其加入因子列表
    if (n > 2) {
        factors.push_back(n);
    }

    return factors;
}

int main() {
    long long num = 1234567890123456789; // 要分解的大数

    std::vector<long long> factors = primeFactors(num);

    // 输出找到的所有质因数
    for (auto factor : factors) {
        std::cout << factor << std::endl;
    }

    return 0;
}

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#include <iostream>
#include <string>
#include <algorithm>

// 大数加法
std::string addLargeNumbers(std::string num1, std::string num2) {
    int carry = 0;
    std::string result = "";

    while (num1.length() < num2.length()) num1 = "0" + num1;
    while (num2.length() < num1.length()) num2 = "0" + num2;

    for (int i = num1.length() - 1; i >= 0; i--) {
        int sum = (num1[i] - '0') + (num2[i] - '0') + carry;
        carry = sum / 10;
        result = std::to_string(sum % 10) + result;
    }

    if (carry) result = std::to_string(carry) + result;

    return result;
}

// 大数减法
std::string subtractLargeNumbers(std::string num1, std::string num2) {
    std::string result = "";
    bool isNegative = false;

    if (num1.length() < num2.length() || (num1.length() == num2.length() && num1 < num2)) {
        std::swap(num1, num2);
        isNegative = true;
    }

    while (num2.length() < num1.length()) num2 = "0" + num2;

    int borrow = 0;
    for (int i = num1.length() - 1; i >= 0; i--) {
        int diff = (num1[i] - '0') - (num2[i] - '0') - borrow;
        if (diff < 0) {
            diff += 10;
            borrow = 1;
        } else {
            borrow = 0;
        }
        result = std::to_string(diff) + result;
    }

    result.erase(0, std::min(result.find_first_not_of('0'), result.size()-1));

    return isNegative ? "-" + result : result;
}

// 大数乘法
std::string multiplyLargeNumbers(std::string num1, std::string num2) {
    if (num1 == "0" || num2 == "0") return "0";

    int n = num1.length();
    int m = num2.length();
    std::string result(n + m, '0');

    for (int i = n - 1; i >= 0; i--) {
        int carry = 0;
        int a = num1[i] - '0';
        for (int j = m - 1; j >= 0; j--) {
            int b = num2[j] - '0';
            int prod = a * b + carry + (result[i + j + 1] - '0');
            carry = prod / 10;
            result[i + j + 1] = (prod % 10) + '0';
        }
        result[i] += carry;
    }

    result.erase(0, std::min(result.find_first_not_of('0'), result.size()-1));
    
    return result;
}

// 大数除法
std::string divideLargeNumbers(std::string dividend, std::string divisor) {
    // 略
    return "To be implemented";
}

int main() {
    std::string num1 = "123456789012345678901234567890";
    std::string num2 = "987654321098765432109876543210";

    std::string sum = addLargeNumbers(num1, num2);
    std::string difference = subtractLargeNumbers(num1, num2);
    std::string product = multiplyLargeNumbers(num1, num2);

    std::cout << "Sum: " << sum << std::endl;
    std::cout << "Difference: " << difference << std::endl;
    std::cout << "Product: " << product << std::endl;

    return 0;
}