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

Input

5 4 1
1 2
1 3
2 4
4 5

Output

0 1 1 2 3

Example 2

Input

6 2 4
2 4
5 6

Output

-1 1 -1 0 -1 -1

Explanation

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