How to sort a vector of pairs in descending order and by the second element?

I am working on a programming challenge and I have already looked at this topics before asking:

Sorting elements of vector where each element is a pair [duplicate]

How do I sort a vector of pairs based on the second element of the pair?

And the situation is like this:

-I have my vector of pairs: vector< pair<int, int> > rank;

-And I have already implemented a predicate to compare and sort the vector of pairs by the second element and in descending order:

struct predicate
{
    bool operator()(const std::pair<int, int> &left, const std::pair<int, int> &right) 
    {
         return left.second < right.second;
    }
}

sort(rank.rbegin(), rank.rend(), predicate());

The programming challenge will give repeated values for the second element, and for that cases, I must leave the first element ordered by the time it was inserted to the vector of pairs, for example:

K V
1 3
2 4
4 5
33 3

Sorted must be:

4 5
2 4
1 3
33 3

The problem comes when I test my solution with a test case I designed:

K V
1 2
16 3
11 2
20 3
18 2
39 39
23 22
12 19
123 4
145 6
3 5
26 4
9574 4
7 1
135 5
193 99
18237 3
22 4
1293 3
3471 33

It's supposed the output should be like this, after sorting the vector:

193 99
39 39
3471 33
23 22
12 19
145 6
3 5
135 5
123 4
26 4
9574 4
22 4
16 3
20 3
18237 3
1293 3
1 2
11 2
18 2
7 1

But instead of that, I got some elements ordered by the first value too:

193 99
39 39
3471 33
23 22
12 19
145 6
3 5
135 5
123 4
26 4
9574 4
22 4
20 3 ->Changed element
16 3 ->Changed element
18237 3
1293 3
18 2 ->Changed element
11 2
1 2 ->Changed element
7 1

Why is happening this?? What am I doing wrong?? Help will be appreciated