You are given a weighted undirected graph on n vertices and m edges. Find the shortest path from vertex s to vertex t or else state that such path doesn't exist. The first line of the input contains two space-separated integers — n and m ( 1 ≤ n ≤ 10 5 ; 0 ≤ m ≤ 10 5 ). Next m lines contain the description of the graph edges. The i -th line contains three space-separated integers — u i , v i , x i ( 1 ≤ u i , v i ≤ n ; 0 ≤ x i ≤ 10 5 ). That means that vertices with numbers u i and v i are connected by edge of length 2 x i (2 to the power of x i ). The last line contains two space-separated integers — the numbers of vertices s and t . The vertices are numbered from 1 to n . The graph contains no multiple edges and self-loops. In the first line print the remainder after dividing the length of the shortest path by 1000000007 (10 9 + 7) if the path exists, and -1 if the path doesn't exist. If the path exists print in the second line integer k — the number of vertices in the shortest path from vertex s to vertex t ; in the third line print k space-separated integers — the vertices of the shortest path in the visiting order. The first vertex should be vertex s , the last vertex should be vertex t . If there are multiple shortest paths, print any of them. A path from vertex s to vertex t is a sequence v 0 , ..., v k , such that v 0 = s , v k = t , and for any i from 0 to k - 1 vertices v i and v i + 1 are connected by an edge. The length of the path is the sum of weights of edges between v i and v i + 1 for all i from 0 to k - 1 . The shortest path from s to t is the path which length is minimum among all possible paths from s to t .