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: Wrong Answer)

/*
　　　  ∧＿∧　やあ
　　 （´・ω・｀)　　　　　/　　　　　ようこそ、バーボンハウスへ。
　　 ／∇y:::::＼　　　 [￣]　　　　　このテキーラはサービスだから、まず飲んで落ち着いて欲しい。
　　 |:⊃:|:::::|　　　|──|
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣|　うん、「また」なんだ。済まない。
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣|￣　  仏の顔もって言うしね、謝って許してもらおうとも思っていない。
￣￣￣￣￣￣￣￣￣￣￣￣￣￣／|
　　　　∇　∇　∇　∇　　　／.／|　　　でも、この提出を見たとき、君は、きっと言葉では言い表せない
　　　　┴　┴　┴　┴　／ ／　  |　　　「ときめき」みたいなものを感じてくれたと思う。
￣￣￣￣￣￣￣￣￣￣|／　　  |　　　殺伐としたコンテストの中で、そういう気持ちを忘れないで欲しい
￣￣￣￣￣￣￣￣￣￣　　　　 |　　　そう思って、この提出を投げたんだ。
　　　(⊆⊇)　(⊆⊇)　(⊆⊇)　　|
　    ||　　 ||　　||　　|　　　 じゃあ、判定を聞こうか。
　　.／|＼　／|＼ ／|＼
*/

#include <iostream>
#include <cstdlib>
#include <algorithm>
#include <array>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstdio>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <vector>
using namespace std;
#define fst first
#define snd second
#define mp make_pair
#define ALL(obj) (obj).begin(),(obj).end()
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define RFOR(i,a,b) for(int i = (b-1);i>=a;i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n) 
#define SIZE(x) ((int)(x).size())
#define debug(x) cerr << #x << " -> " << x << " (line:" << __LINE__ << ")" << '\n';
#define debugpair(x, y) cerr << "(" << #x << ", " << #y << ") -> (" << x << ", " << y << ") (line:" << __LINE__ << ")" << '\n';
typedef long long lint;
typedef pair<int, int> pint;
typedef pair<lint, lint> plint;
typedef vector<lint> vec;
typedef vector<vector<lint>> matrix;
typedef priority_queue<lint> p_que;
typedef priority_queue<lint, vector<lint>, greater<lint>> p_que_rev;
const lint INF = INT_MAX;
const lint LINF = LLONG_MAX;
const lint MOD = 1000000000 + 7;
const double EPS = 1e-9;
const double PI = acos(-1);
const int di[]{0, -1, 0, 1, -1, -1, 1, 1};
const int dj[]{1, 0, -1, 0, 1, -1, -1, 1};

lint gcd(lint a, lint b) {
    lint r;
    while (b != 0) {
        r = a % b;
        a = b; 
        b = r;
    }
    return a;
}

lint lcm(lint a, lint b) {
    return (a / gcd(a, b)) * b;
}

lint power(lint x, lint n, lint mod = MOD) {
    lint ret = 1;
    while(n > 0) {
        if(n & 1){
            (ret *= x) %= mod;
        }
        (x *= x) %= mod;
        n >>= 1;
    }
    return ret;
}

vector<lint> make_power(int n, lint base){
    lint num = 1;
    vector<lint> ret;
    for (int i=0; i<=n; ++i){
        ret.push_back(num);
        num *= base;
    }
    return ret;
}

// Graph Templates
using Weight = lint;
// using Flow = int;
struct Edge {
    int src, dst;
    Weight weight;
    // Flow cap;
    Edge() : src(0), dst(0), weight(0) {}
    Edge(int s, int d, Weight w) : src(s), dst(d), weight(w) {}
};
using Edges = vector<Edge>;
using Graph = vector<Edges>;
using Array = vector<Weight>;
using Matrix = vector<Array>;

// add edge a <--(weight = w)--> b
void add_edge(Graph &g, int a, int b, Weight w) {
    g[a].push_back(Edge(a, b, w));
    g[b].push_back(Edge(b, a, w));
}

// add edge a --(weight = w)--> b
void add_arc(Graph &g, int a, int b, Weight w) { g[a].push_back(Edge(a, b, w)); }

// bellmanFord
// if the graph contains a negative cycle, return negCycle is "true".
pair<vector<Weight>, bool> bellmanFord(const Graph &g, int s) {
    int n = g.size();
    Edges es;
    for (int i = 0; i < n; i++){
        for (auto &e : g[i]){
            es.emplace_back(e);
        }
    }
    vector<Weight> dist(n, -LINF);
    dist[s] = 0;
    bool hasNegCycle = false;
    for (int i = 0;; i++) {
        bool update = false;
        for (auto &e : es) {
            if (dist[e.src] != -LINF && dist[e.dst] < dist[e.src] + e.weight) {
                dist[e.dst] = dist[e.src] + e.weight;
                update = true;
            }
        }
        if (!update) break;
        if (i > n) {
            hasNegCycle = true;
            break;
        }
    }
    return make_pair(dist, hasNegCycle);
}

int main()
{
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    int n, m;
    cin >> n >> m;
    int a, b;
    lint c;
    Graph g(n);
    REP(i, m){
        cin >> a >> b >> c;
        a--;
        b--;
        add_arc(g, a, b, c);
    }
    auto res = bellmanFord(g, 0);
    if(res.snd){
        cout << "inf" << endl;
    }
    else {
        cout << res.fst[n-1] << endl;
    }
    return 0;
}