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 PyPy3 (7.3.0) (judge verdict: Accepted)

import sys
INF = 1 << 60
MOD = 10**9 + 7 # 998244353
sys.setrecursionlimit(2147483647)
input = lambda:sys.stdin.readline().rstrip()
from heapq import heappop, heappush
def resolve():
    n, m = map(int, input().split())
    N = 1 << (n - 1).bit_length()
    N2, N3 = N * 2, N * 3
    E = [[] for _ in range(N * 3 + m)]
    ref = lambda v : v if v < 3 * N else v - N2

    # build range-edge graph
    for i in range(N - 1, 0, -1):
        cl, cr = i << 1, i << 1 | 1
        E[i].append((cl, 0))
        E[i].append((cr, 0))
        E[ref(cl + N2)].append((ref(i + N2), 0))
        E[ref(cr + N2)].append((ref(i + N2), 0))

    # add range-edge
    for i in range(m):
        u, v, w = map(int, input().split())
        u -= 1
        # lower
        l, r = u + N, v + N
        while l < r:
            if l & 1:
                E[ref(l + N2)].append((N3 + i, w))
                l += 1
            if r & 1:
                r -= 1
                E[ref(r + N2)].append((N3 + i, w))
            l >>= 1
            r >>= 1
        # upper
        l, r = u + N, v + N
        while l < r:
            if l & 1:
                E[N3 + i].append((l, 0))
                l += 1
            if r & 1:
                r -= 1
                E[N3 + i].append((r, 0))
            l >>= 1
            r >>= 1

    # Dijkstra (source : N, termination : N + n - 1)
    dist = [INF] * (N3 + m)
    dist[N] = 0
    heap = [(0, N)]
    while heap:
        d, v = heappop(heap)
        if dist[v] != d:
            continue
        for nv, w in E[v]:
            if dist[nv] > d + w:
                dist[nv] = d + w
                heappush(heap, (d + w, nv))

    ans = dist[N + n - 1]
    if ans == INF:
        ans = -1
    print(ans)
resolve()