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: Accepted)

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String {
            bytes
                .by_ref()
                .map(|r| r.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };

    ($next:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };

    ($next:expr, [ $t:tt ]) => {
        {
            let len = read_value!($next, usize);
            (0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
        }
    };

    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };

    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_imports)]
use std::cmp::{min, max};

fn main() {
    input!{
        n: usize,
        m: usize,
        mut v: [(usize1, usize1, usize); m]
    }
    v.sort_by(|x, y| if x.0 == y.0 {x.1.cmp(&y.1)} else {x.0.cmp(&y.0)});
    let mut segt = LSegT::new(n);
    segt.update(0, 0, 0);
    for &(l, r, c) in &v {
        let dm = segt.get(l, r);
        if dm == usize::max_value() {
            break;
        }
        segt.update(l, r, dm + c);
    }
    let d = segt.get(n - 1, n - 1);
    if d == usize::max_value() {
        println!("-1");
    } else {
        println!("{}", d);
    }
}

#[derive(Debug)]
struct LSegT {
    v: Vec<usize>,
    lazy: Vec<Option<usize>>,
    n: usize
}

impl LSegT {
    fn new(n: usize) -> LSegT {
        let mut s = 1;
        while s < n {
            s *= 2;
        }
        LSegT{v: vec![usize::max_value(); 2 * s - 1], lazy: vec![None; 2 * s - 1], n: s}
    }

    fn eval(&mut self, p: usize) {
        if let Some(l) = self.lazy[p] {
            self.v[p] = min(self.v[p], l);
            if p < self.n - 1 {
                self.lazy[2 * p + 1] = Some(self.lazy[2 * p + 1].map_or(l, |x| min(x, l)));
                self.lazy[2 * p + 2] = Some(self.lazy[2 * p + 2].map_or(l, |x| min(x, l)));
            }
            self.lazy[p] = None;
        }
    }

    fn update(&mut self, l: usize, r: usize, x: usize) {
        let n = self.n;
        self.update_rec(l, r, x, 0, 0, n - 1);
    }

    fn update_rec(&mut self, l: usize, r: usize, x: usize, p: usize, pl: usize, pr: usize) {
        self.eval(p);
        if pl > r || pr < l {
            return;
        } else if l <= pl && pr <= r {
            self.lazy[p] = Some(self.lazy[p].map_or(x, |y| min(x, y)));
            self.eval(p);
        } else {
            self.update_rec(l, r, x, 2 * p + 1, pl, (pl + pr - 1) / 2);
            self.update_rec(l, r, x, 2 * p + 2, (pl + pr + 1) / 2, pr);
            self.v[p] = min(self.v[2 * p + 1], self.v[2 * p + 2]);
        }
    }

    fn get(&mut self, l: usize, r: usize) -> usize {
        let n = self.n;
        self.get_rec(l, r, 0, 0, n - 1)
    }

    fn get_rec(&mut self, l: usize, r: usize, p: usize, pl: usize, pr: usize) -> usize {
        self.eval(p);
        if pl > r || pr < l {
            usize::max_value()
        } else if l <= pl && pr <= r {
            self.v[p]
        } else {
            let a = self.get_rec(l, r, 2 * p + 1, pl, (pl + pr - 1) / 2);
            let b = self.get_rec(l, r, 2 * p + 2, (pl + pr + 1) / 2, pr);
            min(a, b)
        }
    }
}