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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;

public class Main {
    public static final long mod = (long)1e9+7;
    public static final long INF = Long.MAX_VALUE/10;
    public static final int inf = Integer.MAX_VALUE/10;

    static void solve(InputReader in, PrintWriter out){
        int n = in.ni();
        int m = in.ni();
        BellmanFord bf = new BellmanFord(n, m, true);
        for (int i = 0; i < m; i++) {
            bf.addEdge(in.ni()-1, in.ni()-1,-in.nl());
        }
        if(bf.bellmanford(0)){
            out.println("inf");
        }else{
            out.println(-bf.dist[n-1]);
        }
    }
    public static class BellmanFord{
        private ArrayList<Edge> edge;
        long[] dist; int v, e;/*v:頂点数,e:辺数*/
        boolean directed;
        public BellmanFord(int v, int e, boolean directed){
            this.directed = directed;
            this.v = v;
            this.e = this.directed?e:2*e;
            edge = new ArrayList<>(this.e);
            dist = new long[v];
            Arrays.fill(dist,INF);
        }
        public boolean bellmanford(int s){//if a negative cycle exists, return true
            dist[s] = 0;
            boolean update;
            for (int j = 0; j < v; j++) {
                update = false;
                for (int i = 0; i < edge.size(); i++) {
                    Edge e = edge.get(i);
                    if(dist[e.from]!=INF && dist[e.to]>dist[e.from]+e.cost){
                        dist[e.to] = dist[e.from]+e.cost;
                        update = true;
                        if(j == v-1){
                            return true;
                        }
                    }
                }
                if(!update) break;
            }
            return false;
        }
        public void addEdge(int from, int to, long cost){
            Edge e = new Edge(from, to, cost);
            edge.add(e);
            if(!this.directed){
                Edge e_rev = new Edge(to, from, cost);
                edge.add(e_rev);
            }
        }
        class Edge{
            int from, to; long cost;
            Edge(int from, int to, long cost){
                this.from = from;
                this.to = to;
                this.cost = cost;
            }
        }
    }

    public static void main(String[] args) throws Exception{
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        solve(in, out);
        out.close();
    }
    public static class InputReader{
        private BufferedReader br;
        private StringTokenizer st;
        public InputReader(InputStream is){
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }
        public String ns(){
            if(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (Exception e){
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }
        public long nl(){
            return Long.parseLong(ns());
        }
        public int ni(){
            return Integer.parseInt(ns());
        }
        public Double nd(){
            return Double.parseDouble(ns());
        }
        public int[] ni(int n){
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }
        public long[] nl(int n){
            long[] a = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }
        public double[] nd(int n){
            double[] a = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }
    }
}