Undiriented graph is given. Find the shortest path from vertex a to vertex b.

Input

The first line contains two integers n and m (1 ≤ n ≤ 100000, 0 ≤ m ≤ 100000) - the number of vertices and edges. The second line contains two integers a and b - the starting and ending point correspondingly. The next m lines describe the edges.

Output

    If the path between a and b does not exist, print -1. Otherwise print in the first line  the length l of the shortest path between these two vertices in number of edges.

Samples