C++: boost ptree relative key

In C++ using ptree from boost, I need to find the relative key to access a.b.c2.e1 from a.b. This key is c2.e1. How can I write a function which finds this relative key?

#include <iostream>
#include <boost/property_tree/ptree.hpp>
#include <boost/property_tree/json_parser.hpp>

using namespace boost::property_tree;

std::string relative_key(const ptree &p1,const ptree &p2)
{
    ??????????????
    // return "b.c2.e1";
}

int main()
{
    ptree pt0;

    pt0.put("a.b.c1",4);
    pt0.put("a.b.c2.e1",4);
    pt0.put("a.b.c4",4);
    pt0.put("a.d",4);
    pt0.put("k.m",4);
    pt0.put("k.n",4);

    ptree &pt_e1=pt0.get_child("a.b.c2.e1");
    ptree &pt_b=pt0.get_child("a.b");

    std::cout<<relative_key(pt_e1,pt_b)<<std::endl;

    return 0;
}