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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    public static void Main()
    {
        int N = NextInt();
        int M = NextInt();
        //Dijkstraみたいな
        Node[] node = new Node[N];
        for (int i = 0; i < N; i++) node[i] = new Node();
        int[] a = new int[M];
        int[] b = new int[M];
        long[] c = new long[M];
        long min_c = 0;
        for (int i = 0; i < M; i++)
        {
            a[i] = NextInt() - 1;
            b[i] = NextInt() - 1;
            c[i] = NextInt();
            min_c = Math.Min(min_c, c[i]);
        }
        for (int i = 0; i < M; i++)
        {
            Edge e = new Edge();
            e.to = b[i];
            e.cost = c[i] - min_c + 1;
            node[a[i]].relate.Add(e);
        }
        PriorityQueue<long, Node> PQ = new PriorityQueue<long, Node>();
        PQ.Enqueue(0, node[0]);
        int count = 0;

        while (PQ.Count != 0)
        {
            count++;
            Node now = PQ.Dequeue();
            now.visit = true;
            foreach (var e_ in now.relate)
            {
                if (node[e_.to].visit && now.cost + e_.cost > node[e_.to].cost)
                {
                    //訪問済みでも大きくできるならINF
                    Console.WriteLine("inf");
                    return;
                }
                if (now.cost + e_.cost > node[e_.to].cost)
                {
                    //更新できるならする
                    node[e_.to].cost = now.cost + e_.cost;
                    node[e_.to].count = now.count + 1;
                    PQ.Enqueue(node[e_.to].cost, node[e_.to]);
                }
            }
        }
        Console.WriteLine(node[N - 1].cost + ((min_c - 1) * node[N - 1].count));
    }
}
public class Node
{
    public List<Edge> relate = new List<Edge>();
    public bool visit = false;
    public long cost = 0;
    public int count = 0;
}
public class Edge
{
    public int to;
    public long cost;
}
public class PriorityQueue<Tkey, Tvalue> where Tkey : IComparable
{
    private static List<Tkey> list = new List<Tkey>();
    private static List<Tvalue> value = new List<Tvalue>();
    public int Count { get; private set; } = 0;
    private static bool Descending;
    public PriorityQueue(bool b = true) { Descending = b; }
    private static int Compare(Tkey a, Tkey b)
    {
        if (Descending) return a.CompareTo(b);
        else return b.CompareTo(a);
    }
    public void Enqueue(Tkey e, Tvalue n)
    {
        Count++;
        int now = Count - 1;
        list.Add(e);
        value.Add(n);
        while (now != 0)
        {
            int par = (now - 1) / 2;
            if (Compare(list[par], e) <= 0) break;
            Tkey a = list[now]; list[now] = list[par]; list[par] = a;
            Tvalue b = value[now]; value[now] = value[par]; value[par] = b;
            now = par;
        }
    }
    public Tvalue Dequeue()
    {
        if (Count == 0) return (Tvalue)(object)(-1);
        Tvalue e = value.First();
        if (Count == 1) { list = new List<Tkey>(); value = new List<Tvalue>(); Count--; return e; }
        Tkey x = list[Count - 1];
        Tvalue y = value[Count - 1];
        int i = 0;
        while (i * 2 + 1 < Count)
        {
            int l = i * 2 + 1;
            int r = i * 2 + 2;
            if (r < Count && Compare(list[r], list[l]) < 0) l = r;
            if (Compare(list[l], x) >= 0) break;
            list[i] = list[l];
            value[i] = value[l];
            i = l;
        }
        list[i] = x;
        value[i] = y;
        Count--;
        return e;
    }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}