BFS Shortest Distances

You are given an undirected graph with $n$ vertices numbered from $1$ to $n$, and a starting vertex $s$.

Find the minimum number of edges needed to reach every vertex from $s$. If a vertex cannot be reached, its distance is -1.

Input

The first line contains three integers $n$, $m$, and $s$: the number of vertices, the number of edges, and the starting vertex.

The next $m$ lines each contain two integers $a$ and $b$, meaning there is an undirected edge between vertices $a$ and $b$.

Output

Print $n$ integers: the distances from $s$ to vertices $1, 2, \ldots, n$, in order. Print -1 for each unreachable vertex.

Constraints

• $1 \le n \le 200000$
• $0 \le m \le 300000$
• $1 \le s \le n$
• $1 \le a, b \le n$

Example 1

5 4 1
1 2
1 3
2 4
4 5

0 1 1 2 3

Example 2

6 2 4
2 4
5 6

-1 1 -1 0 -1 -1

Explanation

Only vertex $2$ is reachable from vertex $4$ in this graph.