I'm a bit confused about stopping at Kth iteration on the Bellman-Ford algorithm to find the shortest path of at most length k from s to t.
Let me show you a graph and explain you what I understand:

[![graph example](https://i.stack.imgur.com/54zOI.png)](https://i.stack.imgur.com/54zOI.png)

At first iteration, I will have:

* Shortest path to get to A is S->A (cost 1)
* Shortest path to get to B is S->B (cost 4)
* Shortest path to get to T is still unknown

At second iteration I will have:

* Shortest path to get to A is S->A (cost 1)
* Shortest path to get to B is A->B (cost 2(A->B) + cost 1(S->A) = 3) **updated!**
* Shortest path to get to T is B->T

But now going to B takes 2 edges instead of 1, so going to T is 3 edges away now: S->A->B->T, and this has happened in 2 iterations.

What am I understanding wrong?