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;

namespace AtCoder
{
    static class Solver
    {
        static IO io = new IO();

        static Node[] nodes;

        public static void Solve()
        {
            io.ReadSplit();
            int N = io.Int();
            int M = io.Int();

            nodes = new Node[N + 1];
            for (int i = 0; i <= N; ++i)
            {
                nodes[i] = new Node();
            }

            for (int i = 0; i < M; ++i)
            {
                io.ReadSplit();
                Edge e = new Edge();
                e.a = io.Int();
                e.b = io.Int();
                e.c = io.Int();
                nodes[e.a].edge_list.Add(e);
                nodes[e.b].reverse_edge_list.Add(e);
            }

            Search_can_reach_N(N);

            if (Check_is_inf(1, N, new List<int>(), new List<int>(), false))
            {
                io.WriteLine("inf");
            }
            else if (Check_is_inf(N, N, new List<int>(), new List<int>(), true))
            {
                io.WriteLine("inf");
            }
            else
            {
                io.WriteLine(Count_total_weight(1, N, new List<int>(), 0, 0).ToString());
            }
        }
        public static void Search_can_reach_N(int b)
        {
            if (nodes[b].can_reach_N)
            {
                return;
            }
            nodes[b].can_reach_N = true;
            foreach (Edge e in nodes[b].reverse_edge_list)
            {
                Search_can_reach_N(e.a);
            }
        }
        public static bool Check_is_inf(int a, int N, List<int> path, List<int> c_locus, bool is_start_from_N)
        {
            if (!nodes[a].can_reach_N)
            {
                return false;
            }
            if (path.Contains(a))
            {
                int cycle_total = 0;
                for (int i = path.IndexOf(a); i < c_locus.Count; ++i)
                {
                    cycle_total += c_locus[i];
                }
                if (cycle_total > 0)
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
            if (a == N)
            {
                if (is_start_from_N)
                {
                    if (path.Contains(N))
                    {
                        return false;
                    }
                }
                else
                {
                    return false;
                }
            }
            path.Add(a);
            foreach (Edge e in nodes[a].edge_list)
            {
                c_locus.Add(e.c);
                if (Check_is_inf(e.b, N, path, c_locus, is_start_from_N))
                {
                    return true;
                }
                c_locus.RemoveAt(c_locus.Count - 1);
            }
            path.RemoveAt(path.Count - 1);
            return false;
        }
        public static long Count_total_weight(int a, int N, List<int> path, long total_c, long max_total_c)
        {
            if (!nodes[a].can_reach_N)
            {
                return long.MinValue;
            }
            if (path.Contains(a))
            {
                return long.MinValue;
            }
            if (a == N)
            {
                return total_c;
            }
            path.Add(a);
            foreach (Edge e in nodes[a].edge_list)
            {
                long new_total_c = Count_total_weight(e.b, N, path, total_c + e.c, max_total_c);
                max_total_c = Math.Max(max_total_c, new_total_c);
            }
            path.RemoveAt(path.Count - 1);
            return max_total_c;
        }
    }
    public class Node
    {
        public List<Edge> edge_list;
        public List<Edge> reverse_edge_list;
        public bool can_reach_N;
        public Node()
        {
            this.edge_list = new List<Edge>();
            this.reverse_edge_list = new List<Edge>();
            this.can_reach_N = false;
        }
    }
    public struct Edge
    {
        public int a;
        public int b;
        public int c;
    }
}
namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            Solver.Solve();
        }
    }
    class IO
    {
        private string[] _Inputs;
        private int _Index;
        public void Read()
        {
            _Inputs = new string[1];
            _Inputs[0] = Console.ReadLine();
            _Index = 0;
        }
        public void ReadSplit()
        {
            _Inputs = Console.ReadLine().Split(' ');
            _Index = 0;
        }
        public string String()
        {
            return _Inputs[_Index++];
        }
        public string[] String(int xCount)
        {
            string[] rv = new string[xCount];
            Array.Copy(_Inputs, _Index, rv, 0, xCount);
            _Index += xCount;
            return rv;
        }
        public int Int()
        {
            return int.Parse(_Inputs[_Index++]);
        }
        public int[] Int(int xCount)
        {
            int[] rv = new int[xCount];
            for (int i = 0; i < xCount; ++i)
            {
                rv[i] = int.Parse(_Inputs[_Index++]);
            }
            return rv;
        }
        public long Long()
        {
            return long.Parse(_Inputs[_Index++]);
        }
        public long[] Long(int xCount)
        {
            long[] rv = new long[xCount];
            for (int i = 0; i < xCount; ++i)
            {
                rv[i] = long.Parse(_Inputs[_Index++]);
            }
            return rv;
        }
        public void Write(string xStr)
        {
            Console.Write(xStr);
        }
        public void WriteLine(string xStr)
        {
            Console.WriteLine(xStr);
        }
    }
}