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 <cstdio>
#include <vector>
#include <algorithm>
using namespace std;
const long long INF=1000000000000000000;

int n,k;
struct dat{
    int s,e,c;
    dat(int S,int E,int C){
        s=S;
        e=E;
        c=C;
    }
};
vector<dat> v;

struct node{
  int s,e,m;
  long long val,lazy;
  node *l,*r;
  node(int _s,int _e){
    s=_s,e=_e,m=(s+e)>>1;
    if (s==e){
    }
    else{
      l=new node(s,m);
      r=new node(m+1,e);
    }
    val=lazy=INF;
  }
  void prop(){
    l->val=min(l->val,lazy);
    r->val=min(r->val,lazy);
  }
  long long query(int i){
    if (s==e) return val;
    else{
        prop();
        if (i<=m) return l->query(i);
        else return r->query(i);
    }
  }
  void update(int i,int j, long long k){
    if (i==s && j==e){
        val=min(val,k);
        lazy=min(lazy,k);
        return;
    }
    else{
        if (j<=m) l->update(i,j,k);
        else if (m<i) r->update(i,j,k);
        else l->update(i,m,k),r->update(m+1,j,k);
        val=min(l->val,r->val);
    }
  }
}*root;


int main(){
    scanf("%d%d",&n,&k);
    int a,b,c;
    while (k--){
        scanf("%d%d%d",&a,&b,&c);
        v.push_back(*new dat(a,b,c));
    }

    sort(v.begin(),v.end(),[](dat &i, dat &j){
        return i.s<j.s;
    });
    root=new node(0,n);
    root->update(1,1,0);

    for (vector<dat>::iterator it=v.begin();it!=v.end();it++){
        root->update((*it).s+1,(*it).e, root->query((*it).s)+(*it).c );
    }

    printf("%lld\n",(root->query(n)==INF)?-1:root->query(n));
}