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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader
import java.io.PrintWriter
import java.lang.StrictMath.*
import java.util.*

var out: PrintWriter = PrintWriter(System.out)  // これを使って出力すると早い
fun main(args: Array<String>) {
    try {
        val nm = ReadLib.readIntArray()

        // from, to
        val MIN = Long.MIN_VALUE
        val d = Array(nm[0] + 1) { MIN }
        d[0] = 0; d[1] = 0

        val edges = mutableListOf<Edge>()
        for (i in 1..nm[1]){
            val abc = ReadLib.readIntArray()
            edges.add(Edge(abc[0], abc[1], abc[2]))
        }

        for (i in 1..nm[0]){
            for (e in edges){
                d[e.toId] = Math.max(d[e.fromId] + e.cost, d[e.toId])
            }
        }

        val nThD = (0 until  d.count()).map { d[it] }.toTypedArray()

        for (e in edges){
            d[e.toId] = Math.max(d[e.fromId] + e.cost, d[e.toId])
        }

        for (i in 0 until  d.count()){
            if (nThD[i] != d[i]){
                out.println("inf")
                return
            }
        }

        out.println(d[nm[0]])

    } finally {
        out.flush()   // 消さない
    }
}

data class Edge(val fromId : Int, val toId : Int, val cost: Int)

/**
 * 読み取り
 */
class ReadLib {
    companion object {
        private var reader: BufferedReader = System.`in`.bufferedReader()

        fun reset() {
            reader = System.`in`.bufferedReader()
        }

        fun readInt(): Int {
            return Integer.parseInt(reader.readLine())
        }

        // Int
        fun readIntArray(delimiters: String = " "): IntArray {
            return reader
                .readLine()
                .split(delimiters)
                .map { s -> Integer.parseInt(s) }
                .toIntArray()
        }

        fun readNTimesInt(n: Int): IntArray {
            return (1..n).map { readInt() }.toIntArray()
        }

        fun readNTimesIntArray(n: Int): Array<IntArray> {
            return (1..n).map { readIntArray() }.toTypedArray()
        }

        // long
        // TODO 別の方法を考える
        fun readLong(): Long {
            return reader.readLine().toLong()
        }

        fun readLongArray(delimiters: String = " "): LongArray {
            return reader.readLine()
                .split(delimiters)
                .map { s -> s.toLong() }
                .toLongArray()
        }

        fun readNTimesLong(n: Int): LongArray {
            return (1..n).map { readLong() }.toLongArray()
        }

        fun readString(): String {
            return reader.readLine()
        }

        fun readStringArray(delimiters: String = " "): Array<String> {
            return readString().split(delimiters).toTypedArray()
        }

        fun readNTimesCharArray(n: Int): Array<CharArray> {
            return (1..n).map { readString().toCharArray() }.toTypedArray()
        }

        fun readNTimesString(n: Int): Array<String> {
            return (1..n).map { readString() }.toTypedArray()
        }

    }
}

/**
 * 要素とその個数を出力
 */
fun <T> Array<T>.ofCountMap(): Map<T, Int> {
    return this.groupBy { it }.mapValues { it.value.count() }
}

/**
 * 文字とその個数を出力
 */
fun String.ofCountMap(): Map<Char, Int> {
    return this.toCharArray().ofCountMap()
}

/**
 * 文字とその個数を出力
 */
fun CharArray.ofCountMap(): Map<Char, Int> {
    return this.groupBy { it }.mapValues { it.value.count() }
}

/**
 * Combination, nCk mod p を求める
 * https://ja.wikipedia.org/wiki/%E3%83%A2%E3%82%B8%E3%83%A5%E3%83%A9%E9%80%86%E6%95%B0
 * http://drken1215.hatenablog.com/entry/2018/06/08/210000
 * @param maxN 最大のn
 * @param mod 素数p
 */
class ModCombination(private val maxN: Int, private val mod: Int = 1000000007) {
    private val fac: IntArray = IntArray(maxN)
    private val finv: IntArray = IntArray(maxN)

    init {
        val inv: IntArray = IntArray(maxN)
        fac[0] = 1
        fac[1] = 1

        inv[0] = 1
        inv[1] = 1
        for (i in 2..maxN) {
            fac[i] = fac[i - 1] * i % mod   // 累積
            // mod % i < i
            inv[i] = mod - ((inv[mod % i].toLong()) * (mod / i) % mod).toInt()
            finv[i] = finv[i - 1] * inv[i] % mod
        }
    }

    /**
     * nCk mod p
     */
    fun Calc(n: Int, k: Int): Int {
        if (n < k || n < 0 || k < 0) {
            return 0
        }

        return ((fac[n].toLong() * finv[k] % mod) * finv[n - k] % mod).toInt()
    }
}

class MyMath {
    companion object {
        // 最大公約数
        fun gcd(m: Long, n: Long): Long {
            var M = m
            var N = n
            while (M % N > 0) {
                val pN = N
                N = M % N
                M = pN
            }

            return N
        }

        fun lcm(m: Long, n: Long): Long {
            return (m / gcd(m, n)) * n
        }

        // 素因数分解（試し割り）
        // http://sucrose.hatenablog.com/entry/2014/10/10/235805
        fun primeFactorization(n: Long): Map<Long, Long> {
            val primes = enumeratePrime(ceil(sqrt(n.toDouble())).toInt())
                .map { it.toLong() }
                .toLongArray()
            primes.sort()

            val counter = mutableMapOf<Long, Long>()
            var cn = n
            for (p in primes) {
                if (cn < p) {
                    break
                }

                while (cn % p == 0L) {
                    counter[p] = counter.getOrElse(p, { 0 }) + 1
                    cn /= p
                }
            }

            if (cn > 1) {
                counter[cn] = 1
            }

            return counter
        }

        // Nまでの素数列挙
        fun enumeratePrime(n: Int): IntArray {
            val isPrime = BooleanArray(n + 1) { true }
            val primes = mutableListOf<Int>()
            for (i in 2..n) {
                if (!isPrime[i]) {
                    continue
                }

                primes.add(i)
                for (j in i..n step i) {
                    isPrime[i] = false
                }
            }

            return primes.toIntArray()
        }
    }
}