Note that time limit has been increased to 3 sec

Mike has 3 arrays $a,b,c$ of length n and a number k. He wants to find minimal value of
$\max_{i = 1}^{n} (((a_i + t) \mod{k}) + ((b_i + t) \mod{k}) + ((c_i + t) \mod{k}))$

over all non-negative integer values of t.

$\textbf{Input}$

The first line contains two numbers n and k ($1 \le n \le 3 \times 10^5,1 \le k \le 10^8$).

Each of the next n lines contains 3 numbers - $a_i,b_i,c_i$ ($0 \le a_i,b_i,c_i < k$).

$\textbf{Output}$

Output the minimal value achievable.