5-Path

You are given a list of edges of an undirected graph. The graph has two special nodes, $a$ and $b$. Find the minimum size of a prefix of this list such that the graph represented by this prefix contains a simple path of 5 edges between nodes $a$ and $b$.

The first line contains two integers $n$ and $m$, the number of nodes and the number of edges in the graph. Each of the following $m$ lines contains two integers $v_i$ and $u_i$, the endpoints of an edge ($1 \le v_i, u_i \le n$). The last line contains two integers $a$ and $b$, the special nodes ($a \neq b$, $1 \le a, b \le n$). The graph has no multiple edges and no self-loops.

If the graph represented by the given edge list contains a simple path of 5 edges, output the answer to the problem. Otherwise, output $-1$.