Given a undirected graph of $n$ vertices and $m$ edges. Find the shortest distance from $1$ to each vertex from $2$ to $n$.
### Input
- The first line contains 2 integers $n, m$.
- The next $m$ lines, each line contains 2 integers $u, v$, there is an edge between those vertices.
### Output
- Print $n - 1$ numbers, $i^{th}$ number is the distance from $1$ to $i + 1$. If there is no way to reach $i + 1$ from $1$, print `-1`.
### Constraints
- $1 \le n, m \le 10^5$.
- $1 \le u, v \le n$.
### Example
Input:
```
5 4
1 2
1 3
2 3
4 5
```
Output:
```
1 1 -1 -1
```
