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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <string>
#include <iostream>
#include <iomanip>
#include <map>
#include <algorithm>
#include <vector>
#include <math.h>
#include <tuple>
#include <queue>
#define INF (long long)1000000007
#define MOD (long long)998244353
using namespace std;



int main(void){
    int n,m;
    cin >> n >> m;
    using P = pair<int,int>;
    vector< P > G[n]; //pair<距離, 行き先>
    vector<long long> dist(n,INF*100000); //sからiの距離
    vector<bool> used(n,false);

    int l,r,c;
    for(int i=0; i<m; i++){
        cin >> l >> r >> c;
        G[l-1].push_back(make_pair(c,r-1));
    }


    priority_queue<P, vector<P>, greater<P> > q;
    while(!q.empty()){
        int d,t;
        tie(d,t)=q.top();q.pop();
        cout << d << " " << t << endl;
    }
    
    q.push( P(0, 0) ); //0 s
    for(int i=1; i<n; i++)G[i].push_back(make_pair(0, i-1));

    //dijkstra
    while(!q.empty()){
        long long d;
        long long t;
        tie(d,t)=q.top();q.pop();
        if(used[t])continue;
        dist[t]=d;
        used[t]=true;
        for( P e: G[t]){
            if(dist[e.second] <= d+e.first)continue;
            q.push( P(d+e.first, e.second));
        }
    }
    if(dist[n-1]==INF*100000)dist[n-1]=-1;
    cout << dist[n-1] << endl;
    
    return 0;
}