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;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((lint)(x).size())
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template<typename T> bool mmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template<typename T> bool mmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template<typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template<typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;
/*
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/tag_and_trait.hpp>
using namespace __gnu_pbds; // find_by_order(), order_of_key()
template<typename TK> using pbds_set = tree<TK, null_type, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename TK, typename TV> using pbds_map = tree<TK, TV, less<TK>, rb_tree_tag, tree_order_statistics_node_update>;
*/

template <typename VAL, typename DVAL>
struct LazySegTree
{
    int N;
    int head;

    vector<VAL> val;
    vector<DVAL> dval;
    VAL I_val;
    DVAL I_dval;

    using vv2v = function<VAL(const VAL&, const VAL&)>;
    using d2d = function<void(DVAL&, const DVAL&)>;
    using d2v = function<void(VAL&, const DVAL&)>;
    vv2v merge_val;
    d2d add_dval;
    d2v refl_dval;

    LazySegTree(vector<VAL> &val_init, VAL val_default, DVAL dval_default,
                vv2v f, d2d dadd, d2v dreflect)
            : N(val_init.size()), I_val(val_default), I_dval(dval_default),
              merge_val(f),
              add_dval(dadd),
              refl_dval(dreflect)
    {
        int N_tmp = 1;
        while (N_tmp < N) N_tmp <<= 1;
        val = vector<VAL>(N_tmp*2, I_val);
        dval = vector<DVAL>(N_tmp*2, I_dval);
        head = N_tmp - 1;
        for (int i=0; i<N; i++) val[head+i] = val_init[i];
        for (int pos=head-1; pos>=0; pos--) val[pos] = merge_val(val[pos*2+1], val[pos*2+2]);
    }

    void resolve_dval(int pos, int l, int r) { // posで遅延を解消して子孫に押し付ける
        refl_dval(val[pos], dval[pos]);
        if (pos < head)
        {
            add_dval(dval[pos*2+1], dval[pos]);
            add_dval(dval[pos*2+2], dval[pos]);
        }
        dval[pos] = I_dval;
    }

    void update(int begin, int end, DVAL dval_q) { update(begin, end, dval_q, 0, 0, head+1); }
    void update(int begin, int end, DVAL dval_q, int pos, int l, int r)
    {
        // 後でリファクタリング
        if (begin <= l && r <= end) { // 担当区間全部使う
            add_dval(dval[pos], dval_q);
            resolve_dval(pos, l, r);
        }
        else if (begin < r && l < end) { // 少なくともどこかで交差
            resolve_dval(pos, l, r);
            update(begin, end, dval_q, pos*2+1, l, (l+r)/2);
            update(begin, end, dval_q, pos*2+2, (l+r)/2, r);
            val[pos] = merge_val(val[pos*2+1], val[pos*2+2]);
        }
        else resolve_dval(pos, l, r);
    }

    VAL getvalue(int begin, int end) { return getvalue(begin, end, 0, 0, head+1); }
    VAL getvalue(int begin, int end, int pos, int l, int r)
    {
        resolve_dval(pos, l, r);
        if (begin <= l && r <= end) return val[pos];
        else if (begin<r && l<end) {
            VAL vl = getvalue(begin, end, pos*2+1, l, (l+r)/2);
            VAL vr = getvalue(begin, end, pos*2+2, (l+r)/2, r);
            val[pos] = merge_val(val[pos*2+1], val[pos*2+2]);
            return merge_val(vl, vr);
        }
        else return I_val;
    }
};

int main()
{
    int N, M;
    cin >> N >> M;
    map<lint, vector<plint>> l2rc;
    REP(_, M)
    {
        lint l, r, c;
        cin >> l >> r >> c;
        l2rc[l - 1].emplace_back(r, c);
    }

    using pib = pair<lint, bool>;
    constexpr lint INF = 1e16;
    vector<lint> v(N, INF);
    v[0] = 0;
    LazySegTree<lint, pib> rmq2(v, INF, pib(INF, false),
                                [](lint a, lint b) { return min(a, b); },
                                [](pib &a, pib b) {if (b.second)
                                {
                                    if (a.second) mmin(a.first, b.first);
                                    else a = b;
                                } },
                                [](lint &a, pib b) {if (b.second) mmin(a, b.first); });

    REP(l, N)
    {
        lint d = rmq2.getvalue(l, l + 1);
        for (auto p : l2rc[l])
        {
            lint r = p.first;
            lint nxt_d = d + p.second;
            rmq2.update(l, r, make_pair(nxt_d, true));
        }
    }
    lint ret = rmq2.getvalue(N - 1, N);
    cout << (ret == INF ? -1 : ret) << endl;
}