CF1555E 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.