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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {

	public static void main(String[] args) {
		try (Scanner scanner = new Scanner(System.in)) {
			int n = scanner.nextInt(), m = scanner.nextInt();
			Path[] paths = new Path[m];
			IntStream.range(0, m).forEach(
					// 最長距離を計算するため、距離をマイナスにする
					i -> paths[i] = new Path(scanner.nextInt() - 1, scanner.nextInt() - 1, -scanner.nextLong()));
			long[] distances = new long[n];
			if (bellmanFord(paths, 0, n, distances)) {
				System.out.println("inf");
			} else {
				System.out.println(-distances[n - 1]);
			}
		}
	}

	/**
	 * https://www.geeksforgeeks.org/bellman-ford-algorithm-dp-23/ を参考に作成
	 * 
	 * @param paths     ノード間の連結パス一覧の配列
	 * @param src       開始ノード
	 * @param n         ノードの数
	 * @param distances 開始ノードから各ノードへの最短距離の配列
	 * @return グラフにはループが含まれているかどうか
	 */
	private static boolean bellmanFord(final Path[] paths, final int src, final int n, final long[] distances) {
		Arrays.fill(distances, Long.MAX_VALUE);
		distances[src] = 0;

		IntStream.range(1, n).forEach(i -> IntStream.range(0, paths.length).forEach(j -> {
			int from = paths[j].from, to = paths[j].to;
			long cost = paths[j].cost;
			if (distances[from] != Long.MAX_VALUE && distances[from] + cost < distances[to]) {
				distances[to] = distances[from] + cost;
			}
		}));
		System.out.println(Arrays.toString(distances));
		// マイナスのループが含まれているかどうかを判定
		// 解説に参考して作成
		boolean[] negative = new boolean[n];
		Arrays.fill(negative, false);
		IntStream.range(0, n).forEach(i -> IntStream.range(0, paths.length).forEach(j -> {
			int from = paths[j].from, to = paths[j].to;
			if (distances[from] != Long.MAX_VALUE && distances[from] + paths[j].cost < distances[to]) {
				distances[to] = distances[from] + paths[j].cost;
				negative[to] = true;
			}
			if (negative[from]) {
				negative[to] = true;
			}
		}));
		return negative[n - 1];
	}

	/**
	 * ノード間の一つのパスを表すクラス
	 */
	private static class Path implements Comparable<Path> {
		/** 開始ノード */
		int from;
		/** 終了ノード */
		int to;
		/** 移動コスト */
		long cost;

		Path(int from, int to, long cost) {
			super();
			this.from = from;
			this.to = to;
			this.cost = cost;
		}

		@Override
		public int compareTo(Path path) {
			long costDiff = this.cost - path.cost;
			return (costDiff > 0) ? 1 : (costDiff < 0) ? -1 : 0;
		}
	}
}