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 Rust (1.15.1) (judge verdict: Accepted)

#[allow(dead_code)]
fn getline() -> String {
    let mut res = String::new();
    std::io::stdin().read_line(&mut res).ok();
    res
}

#[allow(unused_macros)]
macro_rules! readl {
    ($t: ty) => {
        {
            let s = getline();
            s.trim().parse::<$t>().unwrap()
        }
    };
    ($( $t: ty),+ ) => {
        {
            let s = getline();
            let mut iter = s.trim().split(' ');
            ($(iter.next().unwrap().parse::<$t>().unwrap(),)*)
        }
    };
}

#[allow(unused_macros)]
macro_rules! readlvec {
    ($t: ty) => {
        {
            let s = getline();
            let iter = s.trim().split(' ');
            iter.map(|x| x.parse().unwrap()).collect::<Vec<$t>>()
        }
    }
}

#[allow(unused_macros)]
macro_rules! debug { ($x: expr) => { println!("{}: {:?}", stringify!($x), $x) } }
// macro_rules! debug { ($x: expr) => () }

#[allow(dead_code)]
fn show<T>(iter: T) -> String
where
    T: Iterator,
    T::Item: std::fmt::Display
{
    let mut res = iter.fold(String::new(), |sum, e| sum + &format!("{} ", e));
    res.pop();
    res
}

#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{BTreeMap, BinaryHeap, HashMap, HashSet};
#[allow(unused_imports)]
use std::collections::btree_map::Entry::{Occupied, Vacant};

use std::cmp::Ordering;
use std::clone::Clone;
#[derive(Clone, Debug, Hash, Eq, PartialEq)]
struct Edge<Cost>
where
    Cost: std::clone::Clone,
{
    to: usize,
    cost: Cost,
}

impl<Cost> Ord for Edge<Cost>
where
    Cost: Ord + std::clone::Clone,
{
    fn cmp(&self, other: &Edge<Cost>) -> Ordering {
        (self.cost).cmp(&(other.cost)).reverse()
    }
}

impl<Cost> PartialOrd for Edge<Cost>
where
    Cost: std::clone::Clone,
    Edge<Cost>: Ord,
{
    fn partial_cmp(&self, other: &Edge<Cost>) -> Option<std::cmp::Ordering> {
        Some(self.cmp(other))
    }
}

trait Graph
where
    Self::Cost: Clone
{
    type Cost;
    fn len(&self) -> usize;
    fn get<'a>(&'a self, p: usize) -> std::slice::Iter<'a, Edge<Self::Cost>>;
    fn get_order(&self) -> Vec<usize>;
}

#[derive(Clone, Debug, Hash)]
struct AdjList<Cost: Clone> {
    adj: Vec<Vec<Edge<Cost>>>,
}

impl<Cost: Clone> std::ops::Index<usize> for AdjList<Cost> {
    type Output = Vec<Edge<Cost>>;

    fn index(&self, i: usize) -> &Vec<Edge<Cost>> {
        &self.adj[i]
    }
}

impl<Cost: Clone> std::ops::IndexMut<usize> for AdjList<Cost> {
    fn index_mut<'a>(&'a mut self, i: usize) -> &'a mut Vec<Edge<Cost>> {
        &mut self.adj[i]
    }
}

impl<Cost: Clone> AdjList<Cost> {
    fn new(n: usize) -> AdjList<Cost> {
        AdjList {
            adj: vec![vec![]; n],
        }
    }

    fn add_edge(&mut self, from: usize, to_: usize, cost_: Cost) {
        self.adj[from].push(Edge {
            to: to_,
            cost: cost_,
        });
    }

    fn add_uedge(&mut self, from: usize, to_: usize, cost_: Cost) {
        self.add_edge(from, to_, cost_.clone());
        self.add_edge(to_, from, cost_);
    }
}

impl<Cost> Graph for AdjList<Cost>
where
    Cost: Clone
{
    type Cost = Cost;

    fn len(&self) -> usize {
        self.adj.len()
    }

    fn get<'a>(&'a self, p: usize) -> std::slice::Iter<'a, Edge<Cost>> {
        self.adj[p].iter()
    }

    fn get_order(&self) -> Vec<usize> {
        let mut res = Vec::with_capacity(self.len());
        let mut deg = vec![0; self.len()];
        let mut used = vec![false; self.len()];
        for from in 0..self.len() {
            for e in self.get(from) {
                deg[e.to] += 1;
            }
        }
        for s in 0..self.len() {
            if deg[s] != 0 || used[s] {
                continue;
            }
            let mut stack = Vec::new();
            used[s] = true;
            stack.push(s);
            while let Some(p) = stack.pop() {
                used[p] = true;
                res.push(p);
                for e in self.get(p) {
                    deg[e.to] -= 1;
                    if deg[e.to] == 0 {
                        stack.push(e.to);
                    }
                }
            }

        }
        // debug!(deg);
        res
    }
}

trait Zero {
    fn zero() -> Self;
}

impl Zero for i64 {
    fn zero() -> i64 {
        0
    }
}

trait Max {
    fn max_value() -> Self;
}

impl Max for i64 {
    fn max_value() -> i64 {
        std::i64::MAX
    }
}

trait GraphHavingOrderedCost: Graph
where
    Self::Cost: Ord + Add<Self::Cost, Output = Self::Cost> + Zero + Max + Copy,
{
    fn get_shortest_path(&self, from: usize) -> (Vec<Self::Cost>, Vec<usize>);
    fn bellmanford(&self, from: usize) -> (Vec<Self::Cost>, Vec<bool>);
    fn get_shortest_path_graph(&self, from: usize, dist: &Vec<Self::Cost>) -> AdjList<Self::Cost>;
}

use std::ops::Add;
impl<T> GraphHavingOrderedCost for T
where
    T: Graph,
    T::Cost: Ord + Add<T::Cost, Output = T::Cost> + Zero + Max + Copy,
    Edge<T::Cost>: Ord,
{
    fn get_shortest_path(&self, from: usize) -> (Vec<Self::Cost>, Vec<usize>) {
        let n = self.len();

        let mut dist = vec![Self::Cost::max_value(); n];
        let mut pre = vec![n as usize; n];
        let mut heap = std::collections::BinaryHeap::new();
        heap.push(Edge {
            to: from,
            cost: Self::Cost::zero(),
        });
        dist[from] = Self::Cost::zero();
        while let Some(p) = heap.pop() {
            for e in self.get(p.to) {
                if p.cost + e.cost >= dist[e.to] {
                    continue;
                }
                heap.push(Edge {
                    to: e.to,
                    cost: p.cost + e.cost,
                });
                dist[e.to] = p.cost + e.cost;
                pre[e.to] = p.to;
            }
        }
        (dist, pre)
    }

     fn bellmanford(&self, from: usize) -> (Vec<Self::Cost>, Vec<bool>) {
        let n = self.len();
        let mut dist = vec![Self::Cost::max_value(); n];
        let mut updated = vec![true; n];
        dist[from] = Self::Cost::zero();
        for _ in 0..n+1 {
            for e in &mut updated { *e = false; }
            for from in 0..n {
                if dist[from] == Self::Cost::max_value() {
                    continue;
                }
                for e in self.get(from) {
                    if dist[e.to] > dist[from]+e.cost {
                        dist[e.to] = dist[from]+e.cost;
                        updated[e.to] = true;
                    }
                }
            }
        }
        (dist, updated)
    }


    fn get_shortest_path_graph(&self, from: usize, dist: &Vec<Self::Cost>) -> AdjList<Self::Cost> {
        let n = self.len();

        let mut res = AdjList::new(n);
        for from in 0..n {
            for e in self.get(from) {
                if dist[from] + e.cost == dist[e.to] {
                    res.add_edge(from, e.to, e.cost);
                }
            }
        }
        res
    }
}


use std::io::prelude::*;
impl<Cost: Clone> AdjList<Cost> {
    fn vizualize(&self, name: &str) {
        let path = std::path::Path::new("tmp.dot");
        {
            let mut file = std::fs::File::create(path).unwrap();
            let n = self.len();
            file.write_all("digraph graph_name {\n".as_bytes()).unwrap();
            for p in 0..n {
                let s = ["    ".to_string(), p.to_string(), "[];\n".to_string()].connect("");
                file.write_all(s.as_bytes()).unwrap();
            }
            for p in 0..n {
                for e in &self[p] {
                    file.write_all(b"    ").unwrap();
                    file.write_all(p.to_string().as_bytes()).unwrap();
                    file.write_all(b" -> ").unwrap();
                    file.write_all(e.to.to_string().as_bytes()).unwrap();
                    file.write_all(b"\n").unwrap();
                }
            }
            file.write(b"}\n").unwrap();
        }
        let mut cmd = std::process::Command::new("dot");
        cmd.arg("-T");
        cmd.arg("png");
        cmd.arg("tmp.dot");
        cmd.arg("-o");
        cmd.arg(name);
        cmd.status().expect("commend failed to start");
    }
}

fn main() {
    use std::io::Write;
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    macro_rules! printf { ($($arg:tt)*) => (write!(out, $($arg)*).unwrap()); }
    macro_rules! printfln { () => (writeln!(out).unwrap()); ($($arg:tt)*) => (writeln!(out, $($arg)*).unwrap()); }
    
    let (n, m) = readl!(usize, usize);
    let mut g = AdjList::new(n);
    for _ in 0..m {
        let (a, b, c) = readl!(usize, usize, i64);
        g.add_edge(a-1, b-1, -c);
    }
    let (dist, neg) = g.bellmanford(0);
    if neg[n-1] {
        printfln!("inf");
    } else {
        printfln!("{}", -dist[n-1]);
    }
}