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.

Tayyorladi: Azat Yusupov

Text from: e-olimp.com