设置交集和迭代器

Is it possible to have the output of set_intersection or other set_* algorithmic functions be added directly to a type set? So far, I can only think of a way to add directly to something that allows back_inserter.

#include <set>
#include <algorithm>
#include <vector>
#include <iterator>
#include <iostream>
using namespace std;

int main()
{
    // sorted so ok for set operations
    set<int> s = {2, 3, 1};
    set<int> s2 = {1};
    vector<int> v;
    
    set_intersection(s.begin(), s.end(), s2.begin(), s2.end(),
             back_inserter(v));

    copy(v.begin(), v.end(), ostream_iterator<int>(cout, ","));
             
    return 0;
}