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: Accepted)

using Yorukatsu040.Questions;
using Yorukatsu040.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace Yorukatsu040.Questions
{
    /// <summary>
    /// ABC061 D
    /// </summary>
    public class QuestionF : AtCoderQuestionBase
    {
        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nm = inputStream.ReadIntArray();
            var nodeCount = nm[0];
            var edgeCount = nm[1];
            var edges = new Edge[edgeCount];

            for (int i = 0; i < edges.Length; i++)
            {
                var abc = inputStream.ReadIntArray();
                edges[i] = new Edge(abc[0] - 1, abc[1] - 1, -abc[2]);
            }

            var costs = Enumerable.Repeat(1L << 60, nodeCount).ToArray();
            costs[0] = 0;

            for (int i = 0; i < nodeCount; i++)
            {
                foreach (var edge in edges)
                {
                    var newCost = costs[edge.From] + edge.Cost;
                    if (costs[edge.To] > newCost)
                    {
                        costs[edge.To] = newCost;
                        if (i == nodeCount - 1)
                        {
                            // N回目で更新されたらそこは無限ループ
                            costs[edge.To] = -1L << 40;
                        }
                    }
                }
            }

            // 負回路の影響検出
            for (int i = 0; i < nodeCount; i++)
            {
                foreach (var edge in edges)
                {
                    var newCost = costs[edge.From] + edge.Cost;
                    if (costs[edge.To] > newCost)
                    {
                        costs[edge.To] = newCost;
                        if (i == nodeCount - 1 && edge.To == nodeCount - 1)
                        {
                            // 今度こそ間違いなくinf
                            yield return "inf";
                            yield break;
                        }
                    }
                }
            }

            yield return -costs[nodeCount - 1];
        }

        struct Edge
        {
            public int From { get; }
            public int To { get; }
            public long Cost { get; }

            public Edge(int from, int to, long cost)
            {
                From = from;
                To = to;
                Cost = cost;
            }

            public override string ToString() => $"{From}--[{Cost}]-->{To}";
        }
    }
}


namespace Yorukatsu040
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionF();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace Yorukatsu040.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace Yorukatsu040.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion