A14387 | Boring Segments

You are given $n$ segments on a number line, numbered from $1$ to $n$ . The $i$ -th segments covers all integer points from $l_i$ to $r_i$ and has a value $w_i$ .

You are asked to select a subset of these segments (possibly, all of them). Once the subset is selected, it's possible to travel between two integer points if there exists a selected segment that covers both of them. A subset is good if it's possible to reach point $m$ starting from point $1$ in arbitrary number of moves.

The cost of the subset is the difference between the maximum and the minimum values of segments in it. Find the minimum cost of a good subset.

In every test there exists at least one good subset.

The first line contains two integers $n$ and $m$ ( $1 \le n \le 3 \cdot 10^5$ ; $2 \le m \le 10^6$ ) — the number of segments and the number of integer points.

Each of the next $n$ lines contains three integers $l_i$ , $r_i$ and $w_i$ ( $1 \le l_i < r_i \le m$ ; $1 \le w_i \le 10^6$ ) — the description of the $i$ -th segment.

In every test there exists at least one good subset.

Print a single integer — the minimum cost of a good subset.