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 <bits/stdc++.h>

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep_r(i, n) for (int i = n - 1; i >= 0; i--)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define REP(i, n) for (int i = 0, i##_len = (n); i < i##_len; ++i)
#define all(x) (x).begin(), (x).end()
#define SZ(x) ((ll)(x).size())
#define bit(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());

#define INF bit(60)
#define pb push_back
#define mod 1000000007

template <class T>
bool chmax(T &a, const T &b)
{
  if (a < b)
  {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
  if (b < a)
  {
    a = b;
    return 1;
  }
  return 0;
}

using namespace std;
using uif = uint_fast64_t;
using ll = long long int;
using tTree = __gnu_pbds::tree<ll, __gnu_pbds::null_type, less<ll>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

using pa = pair<ll, ll>;

int qp(int a, ll b)
{
  int ans = 1;
  do
  {
    if (b & 1)
      ans = 1ll * ans * a % mod;
    a = 1ll * a * a % mod;
  } while (b >>= 1);
  return ans;
}
int qp(int a, ll b, int mo)
{
  int ans = 1;
  do
  {
    if (b & 1)
      ans = 1ll * ans * a % mo;
    a = 1ll * a * a % mo;
  } while (b >>= 1);
  return ans;
}

int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

#define FACSIZE 2002

ll invfac[FACSIZE];
ll fac[FACSIZE];

ll mod_pow(ll, ll);
ll mod_add(ll, ll);
ll mod_mul(ll, ll);
ll mod_div(ll, ll);
void make_fact(ll);
void make_invfact(ll);

struct edge
{
  ll to;
  ll cost;
};

int main(void)
{
  ll n, m;
  cin >> n >> m;
  vector<ll> L(n);
  vector<ll> R(n);
  vector<ll> C(n);
  rep(i, m) cin >> L[i] >> R[i] >> C[i];

  vector<vector<edge>> graph(n + 1, vector<edge>());
  rep(i, m)
  {
    edge e;
    e.to = R[i];
    e.cost = C[i];
    graph[L[i]].push_back(e);
  }
  for (ll i = n - 1; i > 0; i--)
  {
    edge e;
    e.to = i;
    e.cost = 0;
    graph[i + 1].push_back(e);
  }
  /*
  for (auto v : graph)
  {
    for (auto x : v)
    {
      cout << x.to << "," << x.cost << endl;
    }
  }
  //*/

  vector<ll> dis(n + 1, LLONG_MAX);
  dis[1] = 0;

  priority_queue<pa, vector<pa>, greater<pa>> pque;
  pque.push(make_pair(0, 1));

  while (!pque.empty())
  {
    auto pq = pque.top();
    pque.pop();
    for (auto x : graph[pq.second])
    {
      if (dis[x.to] > dis[pq.second] + x.cost)
      {
        dis[x.to] = dis[pq.second] + x.cost;
        pque.push(make_pair(dis[x.to], x.to));
      }
    }
  }
  /*
  for (auto x : dis)
    cout << x << " ";
  cout << endl;
  //*/
  if (dis[n] == LLONG_MAX)
    cout << -1 << endl;
  else
    cout << dis[n] << endl;

  return 0;
}

ll mod_pow(ll x, ll r)
{
  if (r == 0)
    return 1;
  else if (r == 1)
    return x % mod;
  else if (r % 2 == 0)
  {
    ll t = mod_pow(x, r / 2) % mod;
    return t * t % mod;
  }
  else
  {
    ll t = mod_pow(x, r / 2) % mod;
    ll k = t * t % mod;
    return k * x % mod;
  }
}
ll mod_add(ll a, ll b)
{
  return (a + b) % mod;
}

ll mod_mul(ll a, ll b)
{
  return (a * b) % mod;
}

ll mod_div(ll a, ll b)
{
  return mod_mul(a, mod_pow(b, mod - 2));
}

void make_fact(ll n)
{
  fac[0] = 1;
  rep(i, n)
  {
    fac[i + 1] = mod_mul(fac[i], i + 1);
  }
}

void make_invfact(ll n)
{
  invfac[n] = mod_pow(fac[n], mod - 2);
  for (int i = n - 1; i >= 0; i--)
  {
    invfac[i] = mod_mul(invfac[i + 1], i + 1);
  }
}