Problem:
Score : 400 points

Problem Statement

There is a directed graph with N vertices and M edges.
The i-th edge (1≤i≤M) points from vertex a_i to vertex b_i, and has a weight c_i.
We will play the following single-player game using this graph and a piece.

Initially, the piece is placed at vertex 1, and the score of the player is set to 0.
The player can move the piece as follows:

When the piece is placed at vertex a_i, move the piece along the i-th edge to vertex b_i. After this move, the score of the player is increased by c_i.

The player can end the game only when the piece is placed at vertex N.
The given graph guarantees that it is possible to traverse from vertex 1 to vertex N.

When the player acts optimally to maximize the score at the end of the game, what will the score be?
If it is possible to increase the score indefinitely, print inf.

Constraints

2≤N≤1000

1≤M≤min(N(N-1),2000)

1≤a_i,b_i≤N (1≤i≤M)

a_i≠b_i (1≤i≤M)

a_i≠a_j or b_i≠b_j (1≤i<j≤M)

-10^9≤c_i≤10^9 (1≤i≤M)

c_i is an integer.

In the given graph, there exists a path from vertex 1 to vertex N.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1 c_1
a_2 b_2 c_2
:
a_M b_M c_M

Output

Print the maximum possible score at the end of the game, if it is finite. If it is possible to increase the score indefinitely, print inf.

Sample Input 1

3 3
1 2 4
2 3 3
1 3 5

Sample Output 1

7

There are two ways to move the piece to vertex N=3:

vertex 1 → vertex 2 → vertex 3 : score 4+3=7

vertex 1 → vertex 3 : score 5

Thus, the maximum possible score at the end of the game is 7.

Sample Input 2

2 2
1 2 1
2 1 1

Sample Output 2

inf

It is possible to increase the score indefinitely by alternating between vertex 1 and 2.

Sample Input 3

6 5
1 2 -1000000000
2 3 -1000000000
3 4 -1000000000
4 5 -1000000000
5 6 -1000000000

Sample Output 3

-5000000000

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

/*
    Author:zeke

    pass System Test!
    GET AC!!
*/
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
using ll = long long;
using ld = long double;
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(x) (x).begin(), (x).end()
#define rep3(var, min, max) for (ll(var) = (min); (var) < (max); ++(var))
#define repi3(var, min, max) for (ll(var) = (max)-1; (var) + 1 > (min); --(var))
#define Mp(a, b) make_pair((a), (b))
#define F first
#define S second
#define Icin(s) \
    ll(s);      \
    cin >> (s);
#define Scin(s) \
    ll(s);      \
    cin >> (s);
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;
}
typedef pair<ll, ll> P;
typedef vector<ll> V;
typedef vector<V> VV;
typedef vector<P> VP;
ll mod = 1e9 + 7;
ll MOD = 1e9 + 7;
ll INF = 1e18;
typedef ll Weight;
struct Edge {  //src:辺の始点,dst:辺の終点,weight:辺の重さ
  int src, dst;
  Weight weight;
  Edge(int src, int dst, Weight weight) :
    src(src), dst(dst), weight(weight) { }
};
bool operator < (const Edge &e, const Edge &f) {
  return e.weight != f.weight ? e.weight > f.weight : //辺は重さが重いものを"小さい"と定義する
    e.src != f.src ? e.src < f.src : e.dst < f.dst;
}
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
//引数 g:隣接リスト,s:始点,dist:各頂点までの距離が入る(負閉路を含む場合,-INF),prev:最短路木の親頂点が入る
//戻値 負閉路が存在しない場合:true,そうでないとき:false
bool shortestPath(const Graph &g,int s,vector<Weight> &dist, vector<int> &prev) {
  int n = g.size();
  dist.assign(n, INF+INF); dist[s] = 0;
  prev.assign(n, -2);
  bool negative_cycle = false;
  for(int k=0;k<n;k++){
    for(int i=0;i<n;i++){
      for(auto e=g[i].begin();e!=g[i].end();e++){
        if(dist[e->dst] > dist[e->src] + e->weight) {
          dist[e->dst] = dist[e->src] + e->weight;
          prev[e->dst] = e->src;
          if (k == n-1) {
            dist[e->dst] = -INF;
            negative_cycle = true;
          }
        }
      }
    }
  }
  return !negative_cycle;
}

//引数 prev:最短路木の親頂点集合,t:終点
//戻値 path:sからtへの最短経路
vector<int> buildPath(const vector<int> &prev, int t) {
  vector<int> path;
  for (int u = t; u >= 0; u = prev[u])
    path.push_back(u);
  reverse(path.begin(), path.end());
  return path;
}
Graph g;    //頂点数vの空隣接リストgを生成
ll n,m;
bool dfs(ll now,vector<bool> have){
    if(now==n-1){
        return true;
    }
    for(auto e=g[now].begin();e!=g[now].end();e++){
        ll k=e->dst;
        if(have[k]){
            continue;
        }
        have[k]=true;
        if(dfs(k,have)){
            return true;
        }
    }
    return false;
}
int main(){
  // ...
  cin>>n>>m;
  g.resize(n);
  rep(i,m){
      ll a,b,c;
      cin>>a>>b>>c;
      a--;b--;
      g[a].push_back(Edge(a,b,-c));
  }
  // ...
  // ...
  vector<Weight> dist;
  vector<int> prev;
  bool negative_cycle=shortestPath(g,0,dist,prev);
  if(!negative_cycle){
      rep(i,n){
          if(dist[i]==-INF){
              vector<bool> have(n,false);
              if(dfs(i,have)){
                  cout<<"inf"<<endl;
                  return 0;
              }
          }
      }
  }
  cout<<-dist[n-1]<<endl;
  // ...
}