The shortest path

The undirected 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 ≤ 5 * 10^4, 1 ≤ m ≤ 10^5) - the number of vertices and edges. The second line contains two integers a and b - the starting and ending point correspondingly. 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, and in the second line print l + 1 numbers - the vertices of this path.

Examples