As predicted, a number of students were able to cheat during the last exam, and Doctor Sufyan wanted to avoid that in the future. He wanted to come up with a specific seating order beforehand that guarantees that no two friends will be able to cheat from each other, in case he had to use the meeting room again.
Given the number of students in his class N, which is equal to the number of seats around the table, and the pairs of friends that are likely to cheat from one another, determine whether or not it's possible to find a seating order that guarantees that no cheating incidents will occur.
The first line of input contains two space-separated integers N, M (3 ≤ N ≤ 104) , the number of students (and seats) and the number of cheating pairs of friends, respectively.
Each of the following M lines contains two space-separated integers a b (1 ≤ a, b ≤ N) (a ≠ b), represent a pair of friends that are most likely to cheat.
It is guaranteed that each pair of students will appear at most once.
If it is impossible to find a seating order that guarantees that no cheating incidents will occur, print -1. Otherwise, print N distinct integers, on a single line, representing the seating order of the students around the table.
## Input
The first line of input contains two space-separated integers N, M (3 ≤ N ≤ 104) , the number of students (and seats) and the number of cheating pairs of friends, respectively.Each of the following M lines contains two space-separated integers a b (1 ≤ a, b ≤ N) (a ≠ b), represent a pair of friends that are most likely to cheat.It is guaranteed that each pair of students will appear at most once.
## Output
If it is impossible to find a seating order that guarantees that no cheating incidents will occur, print -1. Otherwise, print N distinct integers, on a single line, representing the seating order of the students around the table.
[samples]
**Definitions**
Let $ N \in \mathbb{Z} $ be the number of students and seats.
Let $ M \in \mathbb{Z} $ be the number of forbidden adjacent pairs (friendships that may lead to cheating).
Let $ G = (V, E) $ be an undirected graph where:
- $ V = \{1, 2, \dots, N\} $ is the set of students (vertices),
- $ E \subseteq \binom{V}{2} $ is the set of edges representing cheating pairs (each $ \{a, b\} \in E $ means students $ a $ and $ b $ are friends and must not be seated adjacently).
**Constraints**
1. $ 3 \leq N \leq 10^4 $
2. $ 0 \leq M \leq \binom{N}{2} $
3. Each edge in $ E $ is unique and undirected: $ \{a, b\} \in E \Rightarrow a \ne b $
4. The seating is a cyclic permutation $ \pi \in S_N $, i.e., a circular arrangement of all $ N $ students.
**Objective**
Determine whether there exists a cyclic ordering $ \pi = (\pi_1, \pi_2, \dots, \pi_N) $ such that for all $ i \in \{1, \dots, N\} $:
$$
\{\pi_i, \pi_{i+1}\} \notin E \quad \text{(with } \pi_{N+1} = \pi_1\text{)}
$$
If such an ordering exists, output any valid $ \pi $. Otherwise, output $-1$.