假设输入的 $x$ 是不超过 $1000$ 的自然数，完成下面的判断题和单选题：

1 2#include <iostream>3using namespace std;4 5const int n = 100000;6const int N = n + 1;7 8int m;9int a[N], b[N], c[N], d[N];10int f[N], g[N];11 12void init()13{14    f[1] = g[1] = 1;15    for (int i = 2; i <= n; i++) {16        if (!a[i]) {17            b[m++] = i;18            c[i] = 1, f[i] = 2;19            d[i] = 1, g[i] = i + 1;20        }21        for (int j = 0; j < m && b[j] * i <= n; j++) {22            int k = b[j];23            a[i * k] = 1;24            if (i % k == 0) {25                c[i * k] = c[i] + 1;26                f[i * k] = f[i] / c[i * k] * (c[i * k] + 1);27                d[i * k] = d[i];28                g[i * k] = g[i] * k + d[i];29                break;30            }31            else {32                c[i * k] = 1;33                f[i * k] = 2 * f[i];34                d[i * k] = g[i];35                g[i * k] = g[i] * (k + 1);36            }37        }38    }39}40 41int main()42{43    init();44 45    int x;46    cin >> x;47    cout << f[x] << ' ' << g[x] << endl;48    return 0;49}