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;
		}
		
		int time = 0;
		int pos = 0;
		for(int i = 0; i < N; i++){
			final int arrival_time = time + (xs[i] - pos);
			final int throught_time = arrival_time + ws[i];
			
			if(arrival_time % (2 * Ts[i]) >= Ts[i]){
				final int arrival_wait_time = (int) ((arrival_time + (2 * Ts[i]) - 1) / (2 * Ts[i]) * (2 * Ts[i]));
				time = arrival_wait_time + ws[i];
			}else if(throught_time % (2 * Ts[i]) >= Ts[i]){
				//System.out.println(throught_time);
				final int arrival_wait_time = (int) ((throught_time + (2 * Ts[i]) - 1) / (2 * Ts[i]) * (2 * Ts[i]));
				//System.out.println(arrival_wait_time);
				time = arrival_wait_time + ws[i];
			}else{
				time = throught_time;
			}
			
			pos = xs[i] + ws[i];
		}
		time += L - (xs[N - 1] + ws[N - 1]);
		
		
		System.out.println(time);
	}
	
}