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 (2.4.0) (judge verdict: Wrong Answer)

import sys
from collections import defaultdict as dd
input = sys.stdin.readline

N, M = map(int, input().split())
d = []


# N: 処理する区間の長さ

INF = 2**31-1

LV = (N).bit_length()
N0 = 2**LV
data = [INF]*(2*N0)
lazy = [None]*(2*N0)

# 伝搬対象の区間を求める
def gindex(l, r):
    L = (l + N0) >> 1; R = (r + N0) >> 1
    lc = 0 if l & 1 else (L & -L).bit_length()
    rc = 0 if r & 1 else (R & -R).bit_length()
    for i in range(LV):
        if rc <= i:
            yield R
        if L < R and lc <= i:
            yield L
        L >>= 1; R >>= 1

# 遅延伝搬処理
def propagates(*ids):
    for i in reversed(ids):
        v = lazy[i-1]
        if v is None:
            continue
        lazy[2*i-1] = data[2*i-1] = lazy[2*i] = data[2*i] = v
        lazy[i-1] = None

def query(l, r):
    propagates(*gindex(l, r))
    L = N0 + l; R = N0 + r

    s = INF
    while L < R:
        if R & 1:
            R -= 1
            s = min(s, data[R-1])
        if L & 1:
            s = min(s, data[L-1])
            L += 1
        L >>= 1; R >>= 1
    return s

# 区間[l, r)をxで更新
def update(l, r, x):
    *ids, = gindex(l, r)
    propagates(*ids)
    f = 0
    if l > 1:
      f = query(l, r)
    #print(f, l, r)
    L = N0 + l; R = N0 + r
    while L < R:
        if R & 1:
            R -= 1
            yl = INF
            if lazy[R-1] != None: yl = lazy[R-1]
            lazy[R-1] = data[R-1] = min(x + f, data[R-1] + x,yl)
        if L & 1:
            yl = INF
            if lazy[L-1] != None: yl = lazy[L-1]
            lazy[L-1] = data[L-1] = min(x + f, data[L-1] + x,yl)
            L += 1
        L >>= 1; R >>= 1
    #print(data)
    for i in ids:
        data[i-1] = min(data[2*i-1], data[2*i])


for _ in range(M):
  d.append(list(map(int, input().split())))
d.sort(key = lambda x: (x[0], x[1]))
#print(d)
for i in range(M):
  update(d[i][0], d[i][1] + 1, d[i][2])
  #print(d[i])
  #print(data)

res = query(N, N + 1)
if res != INF: print(res)
else: print(-1)