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