# Weighted shortest path (2) P13994

Statement

thehtml

Write a program that, given a directed graph with positive costs at the arcs, and two vertices x and y, prints the path of minimum cost that goes from x to y.

Input

Input consists of several cases. Every case begins with the number of vertices n and the number of arcs m. Follow m triples u, v, c, indicating that there is an arc uv of cost c, where uv and 1 ≤ c ≤ 104. Finally, we have x and y. Assume 1 ≤ n ≤ 104, 0 ≤ m ≤ 5n, and that for every pair of vertices u and v there is at most one arc of the kind uv. All numbers are integers. Vertices are numbered from 0 to n−1. If y is reachable from x, you have the guarantee that there is a unique path.

The condition for c was previously c ≤ 1000. It was updated to create new test cases.

Output

For every case, print the path of minimum cost that goes from x to y. If there is no path from ‍x to y, state so.

Public test cases
• Input

```6 10
1 0 6
1 5 15
3 4 3
3 1 8
4 0 20
0 5 5
0 2 1
5 1 10
4 1 2
2 3 4
3 5

2 1
0 1 1000
1 0

3 3
0 2 100
0 1 40
1 2 70
0 2
```

Output

```3 4 1 0 5
no path from 1 to 0
0 2
```
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