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: Runtime Error)

#include <iostream>
#include <utility>
#include <queue>
#define rgi register int
#define pii pair<int,int>
using namespace std;
const int maxn=100005;
const int maxm=200005;
const int inf=1e9+9;
int u[maxm],v[maxm],w[maxm],fst[maxn],nxt[maxm];
int n,m,s,dis[maxn];
bool book[maxn];
priority_queue<pii,vector<pii>, greater<pii> >que;
int main()
{
    ios::sync_with_stdio(false);
    cin>>n>>m>>s;
    for(rgi i=1;i<=m;++i)
    {
        int p,q,r;
        cin>>p>>q>>r;
        if(p==q)
        	continue;
        u[i]=p,v[i]=q,w[i]=r;
        nxt[i]=fst[u[i]];
        fst[u[i]]=i;
    }
    for(rgi i=1;i<=n;++i)
        dis[i]=inf;
    dis[s]=0;
    que.push(make_pair(0,s));
    while(!que.empty())
    {
        int x=que.top().second;
        que.pop();
        if(book[x])
            continue;
        book[x]=1;
        for(rgi i=fst[x];i;i=nxt[i])
            if(dis[v[i]]>dis[u[i]]+w[i])
            {
                dis[v[i]]=dis[u[i]]+w[i];
                que.push(make_pair(dis[v[i]],v[i]));
            }
    }
    if(dis[n]==inf)
    	cout<<"-1"<<endl;
    else
    	cout<<dis[n]<<endl;
    return 0;
}