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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

const int N = (int)1e6+7;
const int INF = (int)1e9+17;
const int mod = 998244353;

typedef long long ll;

int n, m;
ll d[N];
vector<pair<int,int>> g[N];



multiset<ll> dist;
multiset<pair<int,ll>> life_time;

ll getmin(int p) {
    while (!life_time.empty() && life_time.begin()->first < p) {
        dist.erase(dist.find(life_time.begin()->second));
        life_time.erase(life_time.begin());
    }
    if (dist.empty()) {
        cout << -1 << endl;
        exit(0);
    }
    return *dist.begin();
}

void update(int l, int r, ll dist) {
    life_time.insert({r, dist});
    ::dist.insert(dist);
}

int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr), cout.tie(nullptr);
#ifdef LOCAL
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
#endif

    cin >> n >> m;
    vector<int> ls = {1, n};
    for(int i = 0; i < m; ++i) {
        int l, r, x;
        cin >> l >> r >> x;
        g[l].emplace_back(r, x);
        ls.emplace_back(l);
    }
    sort(ls.begin(), ls.end());
    ls.erase(unique(ls.begin(), ls.end()), ls.end());
    for(int v : ls) {
        d[v] = (v == 1 ? 0 : getmin(v));
        for(const auto& e : g[v]) {
            update(v, e.first, d[v] + e.second);
        }
    }
    cout << d[n] << endl;

    return 0;
}