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 bi, ei and wi - the numbers of the ends of i-th edge and its weight correspondingly (1 ≤ bi, ei ≤ n, 0 ≤ wi ≤ 105).

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.