The road network consists of $n$ junctions and $m$ one-way roads, with each road leading from a lower-numbered junction to a higher-numbered junction. Each road has a number. Your task is to find a path from junction $1$ to junction $n$, consisting of at most $d$ edges, on which the maximum of the numbers corresponding to the edges is minimal possible.

The first line contains integers $n, m, d\ (2≤n≤10^5,\ 1≤m,d≤10^5)$. 

The next $m$ lines contain triples of numbers $a_i, b_i, c_i\ (1≤a_i<b_i≤n,\ 0≤c_i≤10^9)$, which mean that there is a road, leading from the junction $a_i$ to the junction $b_i$, which has number $c_i$. For each pair of junctions, there is at most one road that connects them.

On the first line print the number of edges in the selected path $k\ (k≤d)$. 

On the next line print $k+1$ integers, indices of junctions visited by the selected path.

If there is no path from junction $1$ to junction $n$ consisting of at most $d$ edges, print one integer $-1$.