import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.Set;

public class Main {
	
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		final int N = sc.nextInt();
		final long L = sc.nextLong();
		
		int[] xs = new int[N];
		int[] ws = new int[N];
		long[] Ts = new long[N];
		
		for(int i = 0; i < N; i++){
			final int x = sc.nextInt();
			final int w = sc.nextInt();
			final long T = sc.nextLong();
			
			xs[i] = x;
			ws[i] = w;
			Ts[i] = T;
		}
		
		long total_time = 0;
		for(int i = 0; i < N; i++){
			final long arrival_time = total_time + (xs[i] - (i == 0 ? 0 : (xs[i - 1] + ws[i - 1])));
			final long walk_time = Math.max(0, Ts[i] - arrival_time % (2 * Ts[i]));
			
			if(walk_time >= ws[i]){
				total_time = arrival_time + ws[i];
			}else{
				final long arrival_wait_time = (arrival_time + (2 * Ts[i] - 1)) / (2 * Ts[i]) * (2 * Ts[i]);
				total_time = arrival_wait_time + ws[i];
			}
			
			//System.out.println(arrival_time + " " + walk_time + " " + total_time);
		}
		total_time += (L - (xs[N - 1] + ws[N - 1]));
		
		System.out.println(total_time);
	}
	
}