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>
#define ll long long
#define ull unsigned long long

using namespace std;

const ll INF = (long long)1e16;
/// sa bag curatari mai multe
struct AINT {
    vector<ll> val;
    vector<ll> lazy;

    AINT(int sz) {
        lazy.resize(4 * sz + 5, INF);
    }

    void update(ll val, int from, int to, int node, int le, int ri) {
        if(from <= le && ri <= to)
            lazy[node] = min(lazy[node], val);
        else {
            int mid = (le + ri) / 2;
            if(from <= mid)
                update(val, from, to, node * 2, le, mid);
            if(mid < to)
                update(val, from, to, node * 2 + 1, mid + 1, ri);
        }
    }

    ll query(int x, int node, int le, int ri) {
        if(le == ri)
            return lazy[node];

        int mid = (le + ri) / 2;
        if(x <= mid)
            return min(lazy[node], query(x, node * 2, le, mid));
        else
            return min(lazy[node], query(x, node * 2 + 1, mid + 1, ri));
    }

};

int main() {
    //freopen("a.in", "r", stdin);
    //freopen("a.out", "w", stdout);

    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int n, m;
    cin >> n >> m;
    vector<vector<pair<int, ll>>> v(n + 1);
    for(int i = 1; i <= m; i ++) {
        int l, r, cost;
        cin >> l >> r >> cost;
        v[l].push_back({r, cost});
    }

    AINT aint(n);
    aint.update(0, 1, 1, 1, 1, n);
    for(int i = 1; i <= n; i ++) {
        ll current_cost = aint.query(i, 1, 1, n);

        for(auto &it : v[i])
            aint.update(current_cost + it.second, i + 1, it.first, 1, 1, n);
    }

    ll ans = aint.query(n, 1, 1, n);
    if(ans >= INF)
        ans = -1;
    cout << ans;

    return 0;
}