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 Ruby (2.3.3) (judge verdict: Runtime Error)

FROM = 0
TO = 1
COST = 2
MIN_COST = 3

def min(a, b)
  a < b ? a : b
end

def saiki(n_way:, n_cost:)
  target_ways = fetch_target_ways(from: n_way[FROM], to: n_way[TO])

  target_ways.sort_by { |way| way[COST] }.each do |way|
    next unless way[MIN_COST] > n_cost
    way[MIN_COST] = n_cost

    if way[TO] == N
      $min_answer = min($min_answer, n_cost + way[COST])
      next
    end

    way[MIN_COST] = n_cost
    saiki(n_way: way, n_cost: n_cost + way[COST])
  end
end

def fetch_target_ways(from:, to:)
  left = $ways.bsearch_index { |way| way[FROM] >= from + 1 }
  right = $reverse_ways.bsearch_index { |way| way[FROM] <= to }
  return [] if right.nil?
  $ways[left..(M - right - 1)]
end

N, M = gets.split.map(&:to_i)
$ways = M.times.map{ gets.split.map(&:to_i).push(Float::INFINITY) }.sort_by{|way| [way[FROM], way[TO]]}
$reverse_ways = $ways.reverse

$min_answer = Float::INFINITY

saiki(n_way: [0, 1, 0, 0], n_cost: 0)

if $min_answer == Float::INFINITY
  puts -1
else
  puts $min_answer
end