Problem:
Score : 600 points

Problem Statement

We have N points numbered 1 to N arranged in a line in this order.

Takahashi decides to make an undirected graph, using these points as the vertices.
In the beginning, the graph has no edge. Takahashi will do M operations to add edges in this graph.
The i-th operation is as follows:

The operation uses integers L_i and R_i between 1 and N (inclusive), and a positive integer C_i. For every pair of integers (s, t) such that L_i \leq s < t \leq R_i, add an edge of length C_i between Vertex s and Vertex t.

The integers L_1, ..., L_M, R_1, ..., R_M, C_1, ..., C_M are all given as input.

Takahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex 1 to Vertex N in the final graph.

Constraints

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq L_i < R_i \leq N

1 \leq C_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1 C_1
:
L_M R_M C_M

Output

Print the length of the shortest path from Vertex 1 to Vertex N in the final graph.
If there is no shortest path, print -1 instead.

Sample Input 1

4 3
1 3 2
2 4 3
1 4 6

Sample Output 1

5

We have an edge of length 2 between Vertex 1 and Vertex 2, and an edge of length 3 between Vertex 2 and Vertex 4, so there is a path of length 5 between Vertex 1 and Vertex 4.

Sample Input 2

4 2
1 2 1
3 4 2

Sample Output 2

-1

Sample Input 3

10 7
1 5 18
3 4 8
1 3 5
4 7 10
5 9 8
6 10 5
8 10 3

Sample Output 3

28

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
class Program
{
	static long[]S = new long[262144];
	static void Main(string[] args)
	{
		string[] str = Console.ReadLine().Split();
		int N = int.Parse(str[0]);
		int M = int.Parse(str[1]);
		int[][]A = new int[M][];
		for(var i=0;i<M;i++){
			string[] str2 = Console.ReadLine().Split();
			A[i] = new int[3]{int.Parse(str2[0]),int.Parse(str2[1]),int.Parse(str2[2])};
		}
		Array.Sort(A,(x,y)=>x[0].CompareTo(y[0]));
		long INF = 9999999999999999;
		for(var i=0;i<262144;i++){
			S[i] = INF;
		}
		S[131071] = 0;
		for(var i=0;i<M;i++){
			int a = A[i][0]-1;
			int b = A[i][1];
			long c = A[i][2];
			long ia = a+131071;
			long m = S[ia];
			while(ia>0){
				ia = (ia-1)/2;
				m = Math.Min(S[ia],m);
			}
			query(a,b,0,0,131072,m+c);
		}
		int ib = N-1 + 131071;
		long ans = S[ib];
		while(ib>0){
			ib = (ib-1)/2;
			ans = Math.Min(S[ib],ans);
		}
		if(ans==INF){
			ans = -1;
		}
		Console.WriteLine(ans);
	}

	public static int query(int a, int b, int k, int l, int r,long T) {
	if (r <= a || b <= l) return 1000000007;
		if (a <= l && r <= b) {
			S[k] = Math.Min(S[k],T);
			return 0;
		} else {
			int c1 = query(a, b, 2 * k + 1, l, (l + r) / 2, T);
			int c2 = query(a, b, 2 * k + 2, (l + r) / 2, r, T);
			return 0;
		}
	}
}