std::set_intersection, Intersection list with offset

I need get the intersection list between two vectors. And in my case vectors are vector of user type. So to get the number encapsulated I must use a comparer function.

Also I want to able get the intersection with a offSet. For example give two vectors {1,2,3,4,6,8} and {5, 7, 9,10} . Intersection with offSet 2 is { 3,8 } since 3 + 2 = 5 and 8 + 2 = 10.

I suppose the code below should work but instead {3,8} I am getting {3,6,8} . I couldn't figure out how to use comparer function of std::set_intersection. What am I missing?

#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>


struct A 
{
    A ( int in ) { a = in; }
    int getNumber() { return a; }

    bool operator< ( A rhs )
    {
        return this->a < rhs.a;
    }
    int a; 
};

int main()
{
    std::vector<A> v1{1,2,3,4,6,8};
    std::vector<A> v2{5,  7,  9,10};
    int offSet = 2;
    auto lessThanWithOffset = [offSet]( A lhs,  A rhs)
    {
        return lhs.getNumber() + offSet < rhs.getNumber();
    };

    std::sort(v1.begin(), v1.end());
    std::sort(v2.begin(), v2.end());

    std::vector<A> v_intersection;
    std::set_intersection(v1.begin(), v1.end(),
                          v2.begin(), v2.end(),
                          std::back_inserter(v_intersection), lessThanWithOffset);

    for(auto n : v_intersection)
        std::cout << n.getNumber() << ' ';
}