E. Boring Segmentstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint a single integer — the minimum cost of a good subset.ExamplesInput
5 12
1 5 5
3 4 10
4 10 6
11 12 5
10 12 3
Output
3
Input
1 10
1 10 23
Output
0

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

3 
['data structures', 'sortings', 'trees', 'two pointers', '*2100']