WILLIAM BRANGHAM: Roszke, Hungary sits right at this nation's border with Serbia. Here — one week ago — we wade into the river of refugees flowing from the Middle East to Western Europe.

We meet our share of Iraqis, Afghans, North Africans, but most of the people here are Syrians, fleeing their nation's four and a half year old civil war.

People like the Halabi family — Said… His wife, Budal…two young sons, and 14-year-old Maria.

MARIA HALABI: We saw on the news that everyone is traveling this way. So we decided to travel just like them. We've been traveling like two weeks ago. Turkey, Greece, Macedonia, Serbia, and then we're here."

WILLIAM BRANGHAM: Hungary, more so than almost any other European nation is doing everything it can to slow the arrival of these refugees.  But the government just can't build fences fast enough.

The police seem overwhelmed by the task at hand. The camps they build quickly fill to capacity, and so this muddy field is where everyone else gets put.

The "rules" here are changing constantly. One day refugees can cross the path between the fields, the next day they can't.

REFUGEE: I just come to this place for the toilet here, now just I want to go this 100 meters only. They don't let me."

WILLIAM BRANGHAM: We hope to follow the route migrants take from here to points north — to the nations who welcome their arrival — but it's a confusing path.

The Halabi family tries hard to follow the rules…waiting patiently, doing what police ask, cleaning up the trash when they can.  But Said is frustrated.

SAID HALABI:  We do respect the law, and we hope that they understand this.  If there is a procedure, we will follow the procedure. But unfortunately nothing is clear for us.

WILLIAM BRANGHAM: They pack up and wait in line for hours for busses to take them farther north, but not necessarily where they want to go. They'll likely end up stuck in Hungarian processing centers, whose conditions have been described by human rights watch as "abysmal."

But the busses don't come, so it'll be another night sleeping on the ground.

Either way, their goal of getting to Sweden — which they've heard has great schools for their kids — is put off for another day at least.

Others grow impatient with the conditions… and with being held by police. And they chose to break through police lines to set off on foot — maybe hoping for strength and safety in numbers.

After their breakout, the Kador family hides in a field, waiting for nightfall to make a more discreet escape.

In two more days, they'll make it into Austria… sending us photos of them in a refugee center run by the Red Cross.

Next, we leave Hungary's southern border, and drive north towards the capitol —  Budapest — a main transit point for refugees.  It's a 110-mile trip.  But almost immediately, we find those not as lucky as the Kador family.

This is an Afghan family behind me that we were just talking to on the side of the road. They were heading in this direction, toward Szeged. But the police came by, stopped them, and told them now they can't go to the train station as they wanted. They have to be taken to a camp, from which — we've been told — some of these camps mean that you can be stuck for weeks. So they thought they were heading to a train station, eventually on their way to Germany. Now, it's not clear what's gonna happen with them.

Further along the highway to Budapest, we spot two young afghan men taking shelter underneath an overpass.  But traveling out in the open in Hungary without a proper visa or ID usually ends this way:

WILLIAM BRANGHAM: These men Do you know where they will be taken?

POLICE OFFICER: The first police station.

WILLIAM BRANGHAM: To the police station?

POLICE OFFICER: After that, the immigrant camp.

WILLIAM BRANGHAM: To an immigrant camp in Budapest? In Austria?

POLICE OFFICER: Sorry, but I can't give you a record. OK?

WILLIAM BRANGHAM: We've hear smugglers make a fortune plying these roads — picking up refugees at gas stations and rest stops, charging exorbitant rates, and promising safe passage.

On the highway, we pass a few busses with refugees…shuttling them to their next, temporary stop.

I'm at the central train station here in Budapest, Hungary.  Most of the refugees behind me have been bused here or sent on trains from elsewhere in southern Hungary. And now they've been waiting quite a while to take the next train to Vienna, and then further north.

QUESTION: How long have you been waiting here?

REFUGEE: I am from morning, from six morning.

Everyone's penned in close a volunteer shouts instructions in Arabic to move this way or that, to sit down or stand up. But no one seems to pay her much attention.

Hungarians get moved to the front of the lines. They'll get their own carriages, separate from the migrants, once the trains finally do come.

Because of overcrowding, Austria stopped running trains into Hungary, so to make it to the border, there's another transfer, and a two mile walk to the checkpoint.

A few days earlier, this border crossing was barren. On this night, it's a sea of confusion.  Refugees come up to us to ask — is this Austria?  Where will the next bus take us? We're as confused as they are….

POLICE OFFICER: Go Back!

WILLIAM BRANGHAM: Police shout instructions in languages most of the refugees don't speak.

Hameed Yakdi is from Aleppo, Syria — a city assaulted from all sides — by rebels, by ISIS, by the Assad regime.  He fled with his wife, two kids, brother-in-law, and best friend.   And after what they've lived through, the chaos here gets taken in stride.

HAMEED YADKI: Yeah, what we can do?  We learn so many things on this journey. Here, we have, you know, more safety than where we are before. Before we don't know what will come.

WILLIAM BRANGHAM: The Yakdi's — like many of the refugees we meet — still retain their hospitality and warmth, offering us food and a spot on their blanket on the concrete floor where they'll end up sleeping tonight.

HAMEED YADKI: Before, when I am in Aleppo, I have money, but I don't have something to buy. The market, everything empty.

QUESTION: What do you hope for when you go to Germany?

HAMEED YADKI: Really, I don't know, I  just want safe place to stay.

WILLIAM BRANGHAM: The next afternoon, we are in Vienna, and the exhausted Yakdi family makes it here by bus.

Hameed's brother, who's already living in Munich, Germany, has come to meet them.  Thanks to a kind police officer, they'll be permitted to drive away with him, across the Austrian border and on into Germany.

Even on this uncertain road, there are turns of good luck.