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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

fun main(args: Array<String>) {
    val (N, M) = readLine()!!.split(" ").map{it.toInt()}
    val g = Graph(N, 0L, 1e16.toLong()) { a, b -> a + b }

    for (i in 1..M) {
        val (L, R, C) = readLine()!!.split(" ").map{it.toLong()}
        g.edges[L.toInt() - 1].add(Edge(L - 1, R - 1, C))
    }

    for (i in 1 until N) {
        g.edges[i].add(Edge(i, i - 1, 0L))
    }

    val d = dijkstra(g, 0).first

    println(if (d[N - 1] == g.inf) -1 else d[N - 1])
}

data class Edge<T: Comparable<T>>(val from: Int, val to: Int, val weight: T): Comparable<Edge<T>> {
    constructor(from: Long, to: Long, weight: T) : this(from.toInt(), to.toInt(), weight)

    override fun compareTo(other: Edge<T>) = weight.compareTo(other.weight)
}

class Graph<T: Comparable<T>>(val n: Int, val zero: T, val inf: T, val plus: (T, T) -> T) {
    val edges = Array(n) { ArrayList<Edge<T>>() }
}
inline fun <reified T: Comparable<T>>dijkstra(g: Graph<T>, s: Int): Pair<Array<T>, Array<Int>> {
    val N = g.n
    val dist = Array(N) { g.inf }
    val prev = Array(N) {-1}

    val Q = PriorityQueue<Edge<T>>()

    dist[s] = g.zero
    Q.add(Edge(-2, s, g.zero))

    while(Q.isNotEmpty()) {
        val e = Q.peek()
        val v = e.to
        Q.poll()

        if (prev[v] != -1) continue
        prev[v] = e.from
        for (i in g.edges[v]) {
            val d = g.plus(dist[v], i.weight)
            if (dist[i.to] > d) {
                dist[i.to] = d
                Q.add(Edge(i.from, i.to, d))
            }
        }
    }

    return Pair(dist, prev)
}