LogiQuest

16. Shortest Path in a Graph

MediumGraphBFS

Given an undirected, unweighted graph, print the length (number of edges) of the shortest path from s to t, or -1 if t is unreachable.

Input format

Line 1: n m (vertices are numbered 1..n) Next m lines: u v Last line: s t

Output format

The shortest distance or -1.

Example 1

Input

5 5
1 2
2 3
3 4
4 5
1 5
1 4

Output

2

Example 2

Input

4 2
1 2
3 4
1 4

Output

-1

Constraints

1 ≤ n ≤ 10⁵, 0 ≤ m ≤ 2 × 10⁵

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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