Problem Statement

You are given a simple connected undirected graph with $N$ vertices and $M$ edges, where the vertices are numbered $1$ to $N$ and the edges are numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and vertex $v_i$ in both directions.

Initially, there is a piece A on vertex $S$ and a piece B on vertex $T$. Here, $S$ and $T$ are given as input.

You may perform the following operation any number of times in any order:

• Choose either piece A or piece B, and move it from its current vertex to an adjacent vertex via an edge. However, you cannot make a move that results in both pieces ending up on the same vertex.

Your goal is to reach the state in which piece A is on vertex $T$ and piece B is on vertex $S$.

Determine whether this is possible, and if it is, find the minimum number of operations required to achieve it.

Constraints

• $2 \le N \le 2\times 10^5$
• $\displaystyle N-1 \le M \le \min\left(\frac{N(N-1)}{2},\,2\times 10^5\right)$
• $1 \le u_i < v_i \le N$
• The given graph is simple and connected.
• $1 \le S, T \le N$
• $S \neq T$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N M S T
u_1 v_1
u_2 v_2
\vdots
u_M v_M

Output

If it is impossible to achieve the goal, print -1.

If it is possible, print the minimum number of operations required.