Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Quarrel

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFriends Alex and Bob live in Bertown. In this town there are *n* crossroads, some of them are connected by bidirectional roads of equal length. Bob lives in a house at the crossroads number 1, Alex — in a house at the crossroads number *n*.

One day Alex and Bob had a big quarrel, and they refused to see each other. It occurred that today Bob needs to get from his house to the crossroads *n* and Alex needs to get from his house to the crossroads 1. And they don't want to meet at any of the crossroads, but they can meet in the middle of the street, when passing it in opposite directions. Alex and Bob asked you, as their mutual friend, to help them with this difficult task.

Find for Alex and Bob such routes with equal number of streets that the guys can follow these routes and never appear at the same crossroads at the same time. They are allowed to meet in the middle of the street when moving toward each other (see Sample 1). Among all possible routes, select such that the number of streets in it is the least possible. Until both guys reach their destinations, none of them can stay without moving.

The guys are moving simultaneously with equal speeds, i.e. it is possible that when one of them reaches some of the crossroads, the other one leaves it. For example, Alex can move from crossroad 1 to crossroad 2, while Bob moves from crossroad 2 to crossroad 3.

If the required routes don't exist, your program should output -1.

Input

The first line contains two integers *n* and *m* (2 ≤ *n* ≤ 500, 1 ≤ *m* ≤ 10000) — the amount of crossroads and the amount of roads. Each of the following *m* lines contains two integers — the numbers of crossroads connected by the road. It is guaranteed that no road connects a crossroads with itself and no two crossroads are connected by more than one road.

Output

If the required routes don't exist, output -1. Otherwise, the first line should contain integer *k* — the length of shortest routes (the length of the route is the amount of roads in it). The next line should contain *k* + 1 integers — Bob's route, i.e. the numbers of *k* + 1 crossroads passed by Bob. The last line should contain Alex's route in the same format. If there are several optimal solutions, output any of them.

Examples

Input

2 1

1 2

Output

1

1 2

2 1

Input

7 5

1 2

2 7

7 6

2 3

3 4

Output

-1

Input

7 6

1 2

2 7

7 6

2 3

3 4

1 5

Output

6

1 2 3 4 3 2 7

7 6 7 2 1 5 1

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/10/2020 05:56:25 (i1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|