Almost shortest path

Input

First line contains four integers: number of vertices $n$, number of edges $m$ (n, m \le 10^5) and numbers of vertices $s$ and $t$ (1 \le s, t \le n). Each of the next $m$ lines contain two integers $a$ and $b$ that describe an undirected edge $(a,b)$.

Output

Print the length of the almost shortest path between the vertices $s$ and $t$. If such path does not exist, print **-1**.

Examples

Note

 The shortest path between vertices $1$ and $3$ equals to $2$. The edges that the shortest path can go through are highlighted in red. **Almost shortest path** is the shortest path that does not go along any of the red edges. The almost shortest path is highlighted in blue, its length is $5$.