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;
#define pp pair<int,int>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define ll long long
#define ld long double
#define all(a) (a).begin(),(a).end()
#define mk make_pair
ll mod=1000000007;
ll MOD=998244353;
int inf=1000001000;
ll INF=100000000000000000;

#define Int long long
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
 
 
template <typename E>
struct SegmentTree{
  using H = function<E(E,E)>;
  Int n,height;
  H h;
  E ei;
  vector<E> laz;
 
  SegmentTree(H h,E ei):h(h),ei(ei){}
 
  void init(Int n_){
    n=1;height=0;
    while(n<n_) n<<=1,height++;
    laz.assign(2*n,ei);
  }
 
  inline void propagate(Int k){
    if(laz[k]==ei) return;
    laz[(k<<1)|0]=h(laz[(k<<1)|0],laz[k]);
    laz[(k<<1)|1]=h(laz[(k<<1)|1],laz[k]);
    laz[k]=ei;
  }
 
  inline void thrust(Int k){
    for(Int i=height;i;i--) propagate(k>>i);
  }
 
  void update(Int a,Int b,E x){
    thrust(a+=n);
    thrust(b+=n-1);
    for(Int l=a,r=b+1;l<r;l>>=1,r>>=1){
      if(l&1) laz[l]=h(laz[l],x),l++;
      if(r&1) --r,laz[r]=h(laz[r],x);
    }
  }
 
  E get_val(Int a){
    thrust(a+=n);
    return laz[a];
  }
 
  void set_val(Int a,E x){
    thrust(a+=n);
    laz[a]=x;
  }
};
 
//INSERT ABOVE HERE

int main() {
    ll n,m;
    cin >> n >> m;
    auto h=[&](ll x,ll y){return min(x,y);};
  const ll INF = 1e18;
  SegmentTree<ll> seg(h,INF);
  seg.init(n);
  seg.set_val(0,0);
  vector<ll> l(m),r(m),c(m);
  vector<vector<ll>> G(n+1,vector<ll>(0)); 
  rep(i,m){
      cin >> l[i] >> r[i] >> c[i];
      G[--l[i]].push_back(i);
  }
  rep(i,n){
      ll d=seg.get_val(i);
      for (ll j:G[i]) seg.update(l[j],r[j],d+c[j]);
  }
  ll ans=seg.get_val(n-1);
  if (ans>=INF) ans=-1;
  cout << ans << endl;
}