E. Boring Segments
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

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

Examples
Input
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