判断给定的C++代码是否能正确输出指定区间内每个数对应的质因数列表

预期输出形如：{5: [5], 6: [2, 3], 7: [7], 8: [2, 2, 2]}。

int main() {    int n, m;    cin >> n >> m;    if (n > m) swap(n, m);    map<int, vector<int>> prime_factor;    for (int i = n; i <= m; ++i) {        int j = 2, k = i;        while (k != 1) {            if (k % j == 0) {                prime_factor[i] = prime_factor[i] + j;                k /= j;            } else {                ++j;            }        }    }    for (auto& p : prime_factor) {        cout << p.first << ": ";        for (int v : p.second)            cout << v << " ";        cout << endl;    }return 0;
}