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)

// https://atcoder.jp/contests/nikkei2019-2-qual/tasks/nikkei2019_2_qual_d
//
#![allow(unused_imports)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

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

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

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

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

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

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

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

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

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

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! join {
    ($t:expr, $glue:expr) => {
        $t.into_iter().map(|w| w.to_string()).collect::<Vec<_>>().join($glue)
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

// ====

#[derive(Debug, Clone)]
struct Treap<T> {
    root: Link<T>
}

impl<T: Ord + Copy + Debug> Treap<T> {
    fn new() -> Self {
        Treap {
            root: None
        }
    }

    fn push(&mut self, v: T) -> bool {
        if self.contains(v) {
            return false;
        }
        let u = self.root.take();
        self.root = Node::push(u, v);
        true
    }

    fn remove(&mut self, v: T) -> bool {
        Node::remove(&mut self.root, v)
    }

    fn len(&self) -> usize {
        Node::sz(&self.root)
    }

    fn min(&self) -> Option<T> {
        Node::min(&self.root)
    }

    fn max(&self) -> Option<T> {
        Node::max(&self.root)
    }

    fn contains(&self, value: T) -> bool {
        Node::contains(&self.root, value)
    }

    fn peek_less(&self, value: T) -> Option<T> {
        Node::peek_less(&self.root, value)
    }

    fn count_less(&self, value: T) -> usize {
        Node::count_less(&self.root, value)
    }

    fn peek_greater(&self, value: T) -> Option<T> {
        Node::peek_greater(&self.root, value)
    }
}

struct XorShift {
    x: i64,
    y: i64,
    z: i64,
    w: i64
}

impl XorShift {
    fn rotate(&mut self) {
        let t = self.x ^ (self.x << 11);
        self.x = self.y;
        self.y = self.z;
        self.z = self.w;
        self.w = (self.w ^ (self.w >> 19)) ^ (t ^ (t >> 8));
    }

    fn next_i64(&mut self) -> i64 {
        self.rotate();
        self.w
    }
}

static mut RAND: XorShift = XorShift {
    x: 123456789i64,
    y: 362436069i64,
    z: 521288629i64,
    w: 88675123i64
};

fn generate_next() -> i64 {
    let x;
    unsafe {
        x = RAND.next_i64();
    }
    x
}

type Link<T> = Option<Box<Node<T>>>;

#[derive(Debug, Clone)]
struct Node<T> {
    value: T,
    size: usize,
    priority: i64,
    left: Link<T>,
    right: Link<T>,
}

impl<T: Ord + Copy + Debug> Node<T> {
    fn new(value: T) -> Self {
        Node {
            value: value,
            size: 1,
            priority: generate_next(),
            left: None,
            right: None
        }
    }

    fn sz(node: &Link<T>) -> usize {
        match node.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => 0,
            Some(x) => x.size
        }
    }

    fn calc(node: &mut Link<T>) {
        if let Some(x) = node.as_mut() { // TODO: Remove as_mut() after upgrading above 1.26
            x.size = 1 + Node::sz(&x.left) + Node::sz(&x.right);
        }
    }

    fn merge(left: Link<T>, right: Link<T>) -> Link<T> {
        match (left, right) {
            (None, None) => None,
            (None, x) => x,
            (x, None) => x,
            (Some(l), Some(r)) => {
                if l.priority < r.priority {
                    let mut l = l;
                    l.right = Self::merge(l.right.take(), Some(r));
                    let mut l = Some(l);
                    Node::calc(&mut l);
                    l
                } else {
                    let mut r = r;
                    r.left = Self::merge(Some(l), r.left.take());
                    let mut r = Some(r);
                    Node::calc(&mut r);
                    r
                }
            }
        }
    }

    fn min(now: &Link<T>) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None    => None,
            Some(x) => {
                match x.left.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
                    None    => Some(x.value),
                    Some(_) => Self::min(&x.left)
                }
            }
        }
    }

    fn max(now: &Link<T>) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None    => None,
            Some(x) => {
                match x.right.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
                    None    => Some(x.value),
                    Some(_) => Self::max(&x.right)
                }
            }
        }
    }

    fn contains(now: &Link<T>, value: T) -> bool {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => false,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Less    => Self::contains(&x.left, value),
                    Ordering::Equal   => true,
                    Ordering::Greater => Self::contains(&x.right, value)
                }
            }
        }
    }

    fn count_less(now: &Link<T>, value: T) -> usize {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => 0,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Less | Ordering::Equal => {
                        Self::count_less(&x.left, value)
                    },
                    Ordering::Greater => {
                        let w = Self::count_less(&x.right, value);
                        Node::sz(&x.left) + 1 + w
                    }
                }
            }
        }
    }

    fn peek_less(now: &Link<T>, value: T) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => None,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Less | Ordering::Equal => {
                        Self::peek_less(&x.left, value)
                    },
                    Ordering::Greater => {
                        let w = Self::peek_less(&x.right, value);
                        if w == None {
                            Some(x.value)
                        } else {
                            Some(max(w.unwrap(), x.value))
                        }
                    }
                }
            }
        }
    }

    fn peek_greater(now: &Link<T>, value: T) -> Option<T> {
        match now.as_ref() { // TODO: Remove as_ref() after upgrading above 1.26
            None => None,
            Some(x) => {
                match value.cmp(&x.value) {
                    Ordering::Greater | Ordering::Equal => {
                        Self::peek_greater(&x.right, value)
                    },
                    Ordering::Less => {
                        let w = Self::peek_greater(&x.left, value);
                        if w == None {
                            Some(x.value)
                        } else {
                            Some(min(w.unwrap(), x.value))
                        }
                    }
                }
            }
        }
    }

    fn split_at(now: Link<T>, k: usize) -> (Link<T>, Link<T>) {
        match now {
            None => (None, None),
            Some(x) => {
                let mut x = x;
                let lsz = Self::sz(&x.left);
                if k <= lsz {
                    let (nl, nr) = Self::split_at(x.left.take(), k);
                    x.left = nr;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (nl, x)
                } else {
                    let (nl, nr) = Self::split_at(x.right.take(), k-1-lsz);
                    x.right = nl;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (x, nr)
                }
            },
        }
    }

    fn split_by(now: Link<T>, v: T) -> (Link<T>, Link<T>) {
        match now {
            None => (None, None),
            Some(x) => {
                let mut x = x;
                if v <= x.value {
                    let (nl, nr) = Self::split_by(x.left.take(), v);
                    x.left = nr;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (nl, x)
                } else {
                    let (nl, nr) = Self::split_by(x.right.take(), v);
                    x.right = nl;
                    let mut x = Some(x);
                    Node::calc(&mut x);
                    (x, nr)
                }
            },
        }
    }

    fn push(now: Link<T>, new_value: T) -> Link<T> {
        let new_node = Some(Box::new(Node::new(new_value)));
        let (left, right) = Self::split_by(now, new_value);
        Self::merge(Self::merge(left, new_node), right)
    }

    fn remove(now: &mut Link<T>, target_value: T) -> bool {
        let mut both_none = false;
        let w = match now.as_mut() { // TODO: Remove as_mut() after upgrading above 1.26
            None => false,
            Some(x) => {
                if target_value < x.value {
                    Self::remove(&mut x.left, target_value)
                } else if x.value < target_value {
                    Self::remove(&mut x.right, target_value)
                } else {
                    let new_link = Self::merge(x.left.take(), x.right.take());
                    if let Some(node) = new_link {
                        *x = node;
                    } else {
                        both_none = true;
                    }
                    true
                }
            }
        };
        Node::calc(now);
        if both_none {
            now.take();
        }
        w
    }
}

// ====

fn main() {
    input! {
        n: usize, m: usize,
        edges: [(usize1, usize1, i64); m]
    };

    let mut event = vec![vec![]; n];
    for i in 0..m {
        let f = edges[i].0;
        let t = edges[i].1;
        let c = edges[i].2;
        event[f].push((t, c));
    }

    let mut best = 0;

    let mut deq: VecDeque<(usize, i64)> = VecDeque::new();

    let mut treap = Treap::new();
    treap.push((0usize, 0i64));
    for i in 0..n {
        let mut now = -1;
        if let Some((_, b)) = treap.peek_greater((i, -1)) {
            now = b;
        } else {
            continue;
        }
        // debug!(treap);
        // debug!(i, now);

        for &(t, c) in &event[i] {
            let newcost = now+c;
            if let Some((_, b)) = treap.peek_greater((t+1, -1)) {
                if  b <= newcost {
                    continue;
                }
            }
            while let Some((idx, c)) = treap.peek_less((t, -1)) {
                if c >= newcost {
                    treap.remove((idx, c));
                } else {
                    break;
                }
            }
            treap.push((t, newcost));
        }
    }

    if let Some((_, cost)) = treap.peek_greater((n-1, -1)) {
        println!("{}", cost);
    } else {
        println!("-1");
    }
}