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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.UncheckedIOException;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Objects;
import java.util.StringTokenizer;

public class Main {
	static Vertex[] cycle;
	static long[] COST;
	static int N,M;
	static long INF;
	public static void main(String[] args) {
		SC sc = new SC(System.in);
		N=sc.nextInt();
		M=sc.nextInt();
		INF=100_000_000_000_000_000L;
		COST=new long[N+1];
		cycle=new Vertex[N+1];
		for(int i=0; i<=N; i++) {
			cycle[i]=new Vertex();
		}
		for(int i=0; i<M; i++) {
			int from=sc.nextInt();
			int to=sc.nextInt();
			long cost=sc.nextLong();
			cycle[from].add(to, -cost);
		}
		Arrays.fill(COST, INF);
		if(Bellmanford()) {
			pl("inf");
		}
		else {
			pl(-COST[N]);
		}
	}
	public static boolean Bellmanford() {
		COST[0]=0;
		COST[1]=0;
		for(int i=0; i<=N; i++) {
			for(int j=1; j<=N; j++) {
				for(int k=0; k<cycle[j].size(); k++) {
					if(COST[j]!=INF && COST[cycle[j].getKey(k)]>COST[j]+cycle[j].getValue(k)) {
						COST[cycle[j].getKey(k)]=COST[j]+cycle[j].getValue(k);
						if(i==N && cycle[j].getKey(k)==N) {
							return true;
						}
					}
				}
			}
		}
		return false;
	}
	static class SC {
		private BufferedReader reader = null;
		private StringTokenizer tokenizer = null;
		public SC(InputStream in) {
			reader = new BufferedReader(new InputStreamReader(in));
		}
		public String next() {
			if (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new UncheckedIOException(e);
				}
			}
			return tokenizer.nextToken();
		}
		public int nextInt() {
			return Integer.parseInt(next());
		}
		public long nextLong() {
			return Long.parseLong(next());
		}
		public double nextDouble() {
			return Double.parseDouble(next());
		}
		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				throw new UncheckedIOException(e);
			}
		}
	}
	public static void pl(Object o) {
		System.out.println(o);
	}
	public static void pl() {
		System.out.println();
	}
	public static void p(Object o) {
		System.out.print(o);
	}
	public static final class Pair<K, V>{        //powered by mikit

		//Pair<任意の型、任意の型>だが、下の機能すべて使うには、Pair<Integer,Long>でないと不可能
		public K key;
		public V value;
		public Pair(K  key, V value) {
			this.key = key;
			this.value = value;
		}
		public static long getValue(Pair<Integer,Long> a) {
			return a.value;
		}
		public static int getKey(Pair<Integer,Long> a) {
			return a.key;
		}
		public boolean equals(Object o) {
			if (this == o) return true;
			if (o == null || getClass() != o.getClass()) return false;
			Pair<?, ?> pair = (Pair<?, ?>) o;
			return Objects.equals(key, pair.key) &&
					Objects.equals(value, pair.value);
		}
		public int hashCode() {
			return Objects.hash(key, value);
		}
	}
	public static class Vertex{
		ArrayList <Pair<Integer,Long>> rinsetu=new ArrayList<Pair<Integer,Long>>();
		public void add(int V,long cost) {
			rinsetu.add(new Pair<Integer, Long>(V,cost));
		}
		public void show() {        //隣接リストを出力
			for(int i=0; i<rinsetu.size(); i++) {
				System.out.println(rinsetu.get(i));
			}
		}
		public void sort_by_cost() {        //コストの低い順にソートします
			rinsetu.sort(Comparator.comparing(p -> p.value));
		}
		public void sort_by_Vertex() {      //向かう頂点の番号順にソートします
			rinsetu.sort(Comparator.comparing(p -> p.key));
		}
		public long getValue(int i) {
			return Pair.getValue(rinsetu.get(i));   //Valueを取り出す
		}
		public Pair<Integer,Long> get(int i) {
			return rinsetu.get(i);   //Pairをぶっこ抜く
		}
		public int getKey(int i) {
			return Pair.getKey(rinsetu.get(i)); //Valueを取り出す
		}
		public void changeKey(int i,int value) {	//リストのペアの前の値（Key,Value）のKeyを書き換え
			Pair<Integer,Long> tmp=new Pair<Integer, Long>(value,Pair.getValue(rinsetu.get(i)));
			rinsetu.set(i, tmp);
		}
		public void changeValue(int i,long value) {	//リストのペアの後ろの値（Key,Value）のValueを書き換え
			Pair<Integer,Long> tmp=new Pair<Integer, Long>(Pair.getKey(rinsetu.get(i)),value);
			rinsetu.set(i, tmp);
		}
		public void changeKeyValue(int i,int key,long value) {	//リストのペアを書き換え（Key,Valueどちらも）
			Pair<Integer,Long> tmp=new Pair<Integer, Long>(key,value);
			rinsetu.set(i, tmp);
		}
		public int size() {     //次数を返す
			return rinsetu.size();
		}
		public int find_Vertex(int a) {     //ある頂点から本当に特定の辺に行くか？  逐次探索なので速さはお察し
			for(int i=0; i<rinsetu.size(); i++) {
				if(a==Pair.getKey(rinsetu.get(i))) {
					return i;
				}
			}
			return -1;
		}
	}
}