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.Linq;
using System.Collections.Generic;
using Debug = System.Diagnostics.Debug;
using StringBuilder = System.Text.StringBuilder;
using Number = System.Int64;
using static System.Math;
namespace Program
{
    public class Solver
    {
        public void Solve()
        {
            var n = ri;
            var m = ri;
            var G = Enumerate(n, x => new List<Edge>());
            for (int i = 0; i < m; i++)
            {
                var a = ri - 1;
                var b = ri - 1;
                var c = -ri;
                Debug.WriteLine("{0} {1} {2}", a, b, c);
                G[a].Add(new Edge(a, b, c));
            }
            var dist = new long[n];
            if (!G.BellmanFord(0, out dist))
                IO.Printer.Out.WriteLine(-dist[n - 1]);
            else IO.Printer.Out.WriteLine("inf");
        }
        int ri => sc.Integer();
        long rl => sc.Long();
        double rd => sc.Double();
        string rs => sc.Scan();


        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());
        static T[] Enumerate<T>(int n, Func<int, T> f) { var a = new T[n]; for (int i = 0; i < n; ++i) a[i] = f(i); return a; }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex
{
    static public string AsString(this IEnumerable<char> ie) { return new string(System.Linq.Enumerable.ToArray(ie)); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") { return string.Join(st, ie); }
    static public void Main()
    {
        var solver = new Program.Solver();
        solver.Solve();
        Program.IO.Printer.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO
{
    using System.IO;
    using System.Text;
    using System.Globalization;
    public class Printer: StreamWriter
    {
        static Printer() { Out = new Printer(Console.OpenStandardOutput()) { AutoFlush = false }; }
        public static Printer Out { get; set; }
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
        public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
        public void Write<T>(string format, T[] source) { base.Write(format, source.OfType<object>().ToArray()); }
        public void WriteLine<T>(string format, T[] source) { base.WriteLine(format, source.OfType<object>().ToArray()); }
    }
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) return 0;
            if (ptr >= len) { ptr = 0; if ((len = str.Read(buf, 0, 1024)) <= 0) { isEof = true; return 0; } }
            return buf[ptr++];
        }
        public char Char() { byte b = 0; do b = read(); while ((b < 33 || 126 < b) && !isEof); return (char)b; }

        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n'; b = (char)read())
                if (b == 0) break;
                else if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            if (isEof) return long.MinValue;
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != 0 && b != '-' && (b < '0' || '9' < b));
            if (b == 0) return long.MinValue;
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public int Integer() { return (isEof) ? int.MinValue : (int)Long(); }
        public double Double() { var s = Scan(); return s != "" ? double.Parse(s, CultureInfo.InvariantCulture) : double.NaN; }
        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }

        public char[] Char(int n) { return enumerate(n, Char); }
        public string[] Scan(int n) { return enumerate(n, Scan); }
        public double[] Double(int n) { return enumerate(n, Double); }
        public int[] Integer(int n) { return enumerate(n, Integer); }
        public long[] Long(int n) { return enumerate(n, Long); }
    }
}
#endregion
#region Edge
public struct Edge: IComparable<Edge>
{
    public int from, to, id;
    public long cost;
    public Edge(int f, int t) : this() { from = f; to = t; cost = 0; id = -1; }
    public Edge(int f, int t, long v) : this() { from = f; to = t; cost = v; id = -1; }
    public Edge(int f, int t, long v, int idx) : this() { from = f; to = t; cost = v; id = idx; }
    public override string ToString() { return string.Format("{0}->{1}:{2} id:{3}", from, to, cost, id); }
    public int CompareTo(Edge other)
    {
        var cmp = cost.CompareTo(other.cost);
        if (cmp != 0) return cmp;
        cmp = to.CompareTo(other.to);
        if (cmp != 0) return cmp;
        cmp = from.CompareTo(other.from);
        return id.CompareTo(other.id);
    }
}
#endregion
#region bellman_ford
static partial class Graph
{
    //O(|V||E|)
    static public bool BellmanFord(this List<Edge>[] graph, int s, out long[] dist, out int[] prev)
    {
        const long max = 1L << 60;
        var n = graph.Length;
        dist = new long[n];
        prev = new int[n];
        for (int i = 0; i < n; i++)
        {
            dist[i] = max;
            prev[i] = -1;
        }
        dist[s] = 0;
        var negCycle = false;
        for (int i = 0; i < n; i++)
            for (int v = 0; v < n; v++)
                foreach (var np in graph[v])
                {
                    if (dist[np.to] <= np.cost + dist[v])
                        continue;
                    dist[np.to] = np.cost + dist[v];
                    prev[np.to] = v;
                    if (i != n - 1)
                        continue;
                    dist[np.to] = -max;
                    negCycle = true;
                }
        return negCycle;
    }
}

static partial class Graph
{
    static public bool BellmanFord(this List<Edge>[] graph, int s, out long[] dist)
    {
        const long max = 1L << 60;
        var n = graph.Length;
        dist = new long[n];
        for (int i = 0; i < n; i++)
            dist[i] = max;
        dist[s] = 0;
        var negCycle = false;
        for (int i = 0; i < n; i++)
            for (int v = 0; v < n; v++)
                foreach (var np in graph[v])
                {
                    if (dist[np.to] <= np.cost + dist[v])
                        continue;
                    dist[np.to] = np.cost + dist[v];
                    if (i != n - 1)
                        continue;
                    dist[np.to] = -max;
                    negCycle = true;
                }
        return negCycle;
    }
}
static partial class Graph
{
    static public void BellmanFord(this Edge[] edges, int s, long[] dist)
    {
        const long max = 1L << 60;
        var n = dist.Length;
        for (int i = 0; i < n; i++)
            dist[i] = max;
        dist[s] = 0;
        while (true)
        {
            var update = false;
            foreach (var e in edges)
            {
                if (dist[e.from] + e.cost < dist[e.to])
                {
                    dist[e.to] = dist[e.from] + e.cost;
                    update = true;
                }

            }
            if (!update) break;
        }

    }
}
#endregion