Boring Segments

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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

输入输出样例

输入样例 #1

5 12
1 5 5
3 4 10
4 10 6
11 12 5
10 12 3

输出样例 #1

3

输入样例 #2

1 10
1 10 23

输出样例 #2

0