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 Rust (1.15.1) (judge verdict: Time Limit Exceeded)

const INF: i64=std::i64::MAX/2;
fn main() {
    let (n,m) = {
        let t = rv::<usize>();
        (t[0], t[1])
    };
    let mut lrc = Vec::with_capacity(m);
    for _ in 0..m {
        let t = rv::<usize>();
        lrc.push((t[0]-1,t[1]-1,t[2]as i64));
    }
    lrc.sort();
    let f = |v| {
        let mut l=0;
        let mut r=m;
        while l<r {
            let m=(l+r)/2;
            let t=lrc[m].0;
            if t<v {
                l=m+1;
            }
            else if t>v {
                r=m;
            }
            else {
                if m==0 || lrc[m-1].0<v {
                    l=m;
                    r=m;
                }
                else {
                    r=m;
                }
            }
        }
        l
    };
    let mut q = std::collections::BinaryHeap::new();
    q.push((INF-0,n-0));
    let mut d = vec![INF;n];
    while let Some((s,v)) = q.pop() {
        let s=INF-s;
        let v=n-v;
        if d[v]<=s {continue;}
        d[v]=s;
        if v==n-1 {break;}
        let mut i = f(v);
        while i<m && lrc[i].0==v {
            let (_,r,c) = lrc[i];
            if r>=n-1 {
                q.push((INF-(s+c),n-(n-1)));
            }
            let mut j = std::cmp::min(m-1,f(r+1));
            while lrc[j].0>v {
                if lrc[j].0<=r {
                    let (l,r,_)=lrc[j];
                    if d[r]>s+c {
                        q.push((INF-(s+c),n-l));
                    }
                }
                if j==0 {break;}
                j-=1;
            }
            i+=1;
        }
    }
    let t = d[n-1];
    println!("{}",if t<INF {t} else {-1});
}
fn rl() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s
}
fn rv<T>() -> Vec<T>
  where T: std::str::FromStr, T::Err: std::fmt::Debug, {
    rl().split_whitespace().map(|x|x.parse::<T>().unwrap()).collect()
}