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**Task** | Statistics

Time limit: | 1.00 s | Memory limit: | 512 MB |

A game has $n$ levels and $m$ teleportes between them. You win the game if you move from level $1$ to level $n$ using every teleporter exactly once.

Can you win the game, and what is a possible way to do it?

The first input line has two integers $n$ and $m$: the number of levels and teleporters. The levels are numbered $1,2,\dots,n$.

Then, there are $m$ lines describing the teleporters. Each line has two integers $a$ and $b$: there is a teleporter from level $a$ to level $b$.

Print $m+1$ integers: the sequence in which you visit the levels during the game. You can print any valid solution.

If there are no solutions, print "IMPOSSIBLE".

- $2 \le n \le 10^5$

- $1 \le m \le 2 \cdot 10^5$

- $1 \le a,b \le n$

Input:

`5 6`

1 2

1 3

2 4

2 5

3 1

4 2

Output:

`1 3 1 2 4 2 5`