Large Factorial

#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <cmath>
#include <algorithm>
using namespace std;
int main() {
    ifstream fin("input.txt");
    int num;
    fin >> num;
    vector<int> v = { 1 };
    vector<int> v_mul = { 0 };
    int carry = 0;
    for (int i = 2; i <= num; ++i) {
        carry = 0;
        int size = to_string(i).length() + 1;
        for (int j = 0; j < size; ++j) v_mul.push_back(0);
        for (int j = 0; j < v.size(); ++j) {
            carry += v[j] * i;
            v_mul[j] = carry % 10;
            carry /= 10;
        }
        v_mul[v.size()] = carry;
        int k = v.size();
        while (carry > 0) {
            v_mul[k] = carry % 10;
            carry /= 10;
            ++k;
        }
        while (v_mul[v_mul.size() - 1] == 0) {
            v_mul.pop_back();
        }
        v = v_mul;
        v_mul = { 0 };
        v_mul.resize(v.size());
    }
    ofstream cout("output.txt");
    reverse(v.begin(), v.end());
    for (auto el : v) {
        cout << el;
    }
    cout << endl;
    cout.close();
    fin.close();
    system("pause");
}