C++75分求助！

以下是C++高精度代码：

#include <iostream>
#include <vector>

using namespace std;

const int BASE = 100000000;
const int WIDTH = 8;

vector<int> operator+(const vector<int>& a, const vector<int>& b) {
    vector<int> c;
    int t = 0;
    for (int i = 0; i < a.size() || i < b.size(); i++) {
        if (i < a.size()) t += a[i];
        if (i < b.size()) t += b[i];
        c.push_back(t % BASE);
        t /= BASE;
    }
    if (t) c.push_back(1);
    return c;
}

vector<int> operator*(const vector<int>& a, int b) {
    vector<int> c;
    int t = 0;
    for (int i = 0; i < a.size(); i++) {
        t += a[i] * b;
        c.push_back(t % BASE);
        t /= BASE;
    }
    while (t) {
        c.push_back(t % BASE);
        t /= BASE;
    }
    return c;
}

void print(const vector<int>& a) {
    printf("%d", a.back());
    for (int i = a.size() - 2; i >= 0; i--) {
        printf("%08d", a[i]);
    }
}

int main() {
    int n;
    cin >> n;

    vector<int> s(1, 1);
    vector<int> factorial(1, 1);

    for (int i = 2; i <= n; i++) {
        factorial = factorial * i;
        s = s + factorial;
    }

    print(s);

    return 0;
}

以前不会CPP高精打表水过，现在用vector重载了+和*运算符，为什么75分，#4输出了一连串负数？