The Shortest Path
The undirected weighted graph is given. Find the shortest path between two given vertices.
Input
The first line contains two positive integers n and m (n ≤ 2000, m ≤ 50000) - the number of vertices and edges in a graph. The second line contains positive integers s and f (1 ≤ s, f ≤ n, s ≠ f) - the numbers of the vertices, the minimal length between which must be found. Each of the next m lines contains three numbers b[i], e[i] and w[i] - the numbers of the ends of i-th edge and its weight correspondingly (1 ≤ b[i], e[i] ≤ n, 0 ≤ w[i] ≤ 10^5).
Output
Print in the first line one number - the length of minimal path between the vertices s and f. Print in the second line all the vertices on the shortest path from s to f in the traversal order. If the path from s to f does not exist, print -1.
