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.PriorityQueue

fun main(args: Array<String>) {
    val (N, M) = readInputLine().split(" ").map { it.toInt() }
    
    val edges = Array(N) { mutableListOf<Pair<Int, Long>>() }

    for (i in N - 1 downTo 1) {
        edges[i].add(Pair(i - 1, 0L))
    }

    for (i in 1..M) {
        val (L, R, C) = readInputLine().split(" ").map { it.toInt() }
        edges[L - 1].add(Pair(R - 1, C.toLong()))
    }
    
    val cost = LongArray(N) { Long.MAX_VALUE }
    cost[0] = 0L
    val queue = PriorityQueue<Pair<Int, Long>>(N) { x, y -> x.second.compareTo(y.second) }
    
    queue.add(Pair(0, 0L))
    
    while (!queue.isEmpty()) {
        val (s, c) = queue.poll()!!
        
        if (cost[s] < c) {
            continue
        }
        
        for ((ed, ec) in edges[s]) {
            if (cost[ed] > cost[s] + ec) {
                cost[ed] = cost[s] + ec
                queue.add(Pair(ed, cost[ed]))
            }
        }
    }

    if (cost[N - 1] == Long.MAX_VALUE) {
        println(-1)
    } else {
        println(cost[N - 1])
    }
}

fun readInputLine(): String {
    return readLine()!!
}