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: Wrong Answer)

import java.math.*

fun main(args: Array<String>) {
    val (N, M) = readInputLine().split(" ").map { it.toInt() }
    
    val route = mutableListOf<Triple<Int, Int, Long>>()
    
    for (i in 1..M) {
        val (L, R, C) = readInputLine().split(" ").map { it.toInt() }
        route.add(Triple(L - 1, R - 1, C.toLong()))
    }
    
    route.sortBy { it.second }
    route.sortBy { it.first }
    
    var size = 1
    while (size < N) {
        size *= 2
    }
    
    val segTree = LongArray(size * 2 - 1) { Long.MAX_VALUE }
    
    fun update(x: Int, value: Long) {
        var tmp = x + size - 1
        
        segTree[tmp] = value
        while (tmp > 0) {
            tmp = (tmp - 1) / 2
            segTree[tmp] = Math.min(segTree[2 * tmp + 1], segTree[2 * tmp + 2])
        }
    }
    
    fun getMin(a: Int, b: Int, k: Int = 0, l: Int = 0, r: Int = size): Long {
        if (r <= a || b <= l) {
            return Long.MAX_VALUE
        }
        if (a <= l && r <= b) {
            return segTree[k]
        }
        
        val vl = getMin(a, b, 2 * k + 1, l, (l + r) / 2)
        val vr = getMin(a, b, 2 * k + 2, (l + r) / 2, r)
        
        return Math.min(vl, vr)
    }
    
    update(0, 0L)

    for (r in route) {
        val (L, R, C) = r

        val nowCost = getMin(L, R + 1)
        
        if (nowCost == Long.MAX_VALUE) {
            break
        }

        if (segTree[R + size - 1] > nowCost + C) {
            update(R, nowCost + C)
        }
    }

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

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