C++ :: Map To Access Elements Through Multiple Key Values

I used to use map to access elements. map has a good feature that it sort the element automatically. Now I need a map which can access element through multiple key values. So I choosed boost::multi_index_container. I defined a container as follows.

struct elem {
int a,b;
elem(int aa,int bb):a(aa),b(bb) {}
};

typedef multi_index_container <

[Code] ....

What I am wondering is whether boost::multi_index_container can sort elements automatically. Specifically, are all elements extracted through iterator from begin to end shown below having b values between 2 and 100?

test t;
test::iterator begin = t.lower_bound(make_tuple(1,2));
test::iterator end = t.upper_bound(make_tuple(1,100));