import java.io.PrintWriter;
import java.util.Scanner;

public class Main{
	public static void main(String[] args) {
		Scanner scanner=new Scanner(System.in);
		PrintWriter out=new PrintWriter(System.out);
		int n=scanner.nextInt();
		int l=scanner.nextInt();
		int[] x=new int[n];
		int[] w=new int[n];
		int[] t=new int[n];
		for(int i=0; i<n; i++) {
			x[i]=scanner.nextInt();
			w[i]=scanner.nextInt();
			t[i]=scanner.nextInt();
		}
		int p=0;
		for(int i=0; i<n; i++) {
			if(i==0) p+=x[i];
			else p+=x[i]-(x[i-1]+w[i-1]);
			if(p/(2*t[i])%2==1) {
				p=(p/(2*t[i])+1)*2*t[i]+w[i];
			}else {
				int p0=p/(2*t[i])*2*t[i];
				if(t[i]-(p-p0)<w[i]) {
					p=p0+2*t[i]+w[i];
				}else {
					p+=w[i];
				}
			}
		}
		p+=l-(x[n-1]+w[n-1]);
		out.println(p);
		out.close();
		scanner.close();
	}
}