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(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
 
/// Equivalent to std::lowerbound and std::upperbound in c++
pub trait BinarySearch<T> {
    fn lower_bound(&self, &T) -> usize;
    fn upper_bound(&self, &T) -> usize;
}
 
impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
 
    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();
 
        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}
 
 
 
 
 
 
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
 
#[derive(PartialEq, Eq)]
pub struct point(i64, i64, i64);
impl Ord for point {
    fn cmp(&self, other: &point) -> Ordering {
        self.0.cmp(&other.0)
    }
}
 
impl PartialOrd for point {
    fn partial_cmp(&self, other: &point) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}
/*
impl PartialEq for point {
    fn eq(&self, other: &point) -> bool {
        self.0 == other.0
    }
}
impl Eq for point {
    fn eq(&self, other: &point) -> bool {
        self.0 == other.0
    }s
}*/
type P = (i64 , i64);
fn bfs(start:&P, goal:&P, map:&Vec<Vec<char>>) -> i64 {
        let dx = vec![1, 0, -1, 0];
        let dy = vec![0, 1, 0, -1];
        let s = (start.0, start.1);
        let g = (goal.0 , goal.1);
        let mut queue:VecDeque<P> = VecDeque::new();
        let mut d:Vec<Vec<i64>> = Vec::new();
        for i in 0..map.len(){
            d.push(Vec::new());
            for j in 0..map[i].len(){
                d[i].push(30000000);
            }
        }
        queue.push_back((s.0, s.1));
        d[s.0 as usize][s.1 as usize] = 0;
        while(queue.len()!=0){
            let mut p:P = queue[0];
            queue.pop_front();
            if p.0 == g.0 && p.1 == g.1{break;}
            for i in 0..4{
                let nx = p.0 + dx[i];
                let ny = p.1 + dy[i];
                if (0<=nx && nx <map.len() as i64 && 0<=ny &&ny<map[0].len() as i64 && map[nx as usize][ny as usize]!='#' && d[nx as usize][ny as usize] == 30000000 ){
                    queue.push_back((nx, ny));
                    d[nx as usize][ny as usize] = d[p.0 as usize][p.1 as usize] + 1;
                }
            }
 
        }
        d[goal.0 as usize][goal.1 as usize]
}
 
fn bfs01(start:&P, goal:&P, map:&Vec<Vec<char>>) -> i64 {
        let dx = vec![1, 0, -1, 0];
        let dy = vec![0, 1, 0, -1];
        let s = (start.0, start.1);
        let g = (goal.0 , goal.1);
        let mut queue:VecDeque<P> = VecDeque::new();
        let mut d:Vec<Vec<i64>> = Vec::new();
        for i in 0..map.len(){
            d.push(Vec::new());
            for j in 0..map[i].len(){
                d[i].push(30000000);
            }
        }
        queue.push_back((s.0, s.1));
        d[s.0 as usize][s.1 as usize] = 0;
        while(queue.len()!=0){
            let mut p:P = queue[0];
            queue.pop_front();
            if p.0 == g.0 && p.1 == g.1{break;}
            for i in 0..4{
                let nx = p.0 + dx[i];
                let ny = p.1 + dy[i];
                if (0<=nx && nx <map.len() as i64 && 0<=ny &&ny<map[0].len() as i64 && d[nx as usize][ny as usize] == 30000000 ){
                    if map[nx as usize][ny as usize] == '#'{
                        queue.push_back((nx, ny));
                        d[nx as usize][ny as usize] = d[p.0 as usize][p.1 as usize] + 1;
                    }
                    else{
                        queue.push_front((nx, ny));
                        d[nx as usize][ny as usize] = d[p.0 as usize][p.1 as usize];
                    }
                }
            }
 
        }
        d[goal.0 as usize][goal.1 as usize]
}
struct UnionFind_W{
    par:Vec<usize>,
    rank:Vec<usize>,
    size:Vec<usize>,
    diff_weight:Vec<i64>,    
}
impl UnionFind_W{
    fn init(n:usize) -> UnionFind_W{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;    
        }
        UnionFind_W{
            par:par,
            rank:vec![0;n], 
            size:vec![1;n], 
            diff_weight:vec![0i64;n],
        }
    }
    fn find(&mut self, x:usize) ->usize{
        if(self.par[x] == x){
            x    
        }
        else{
            let p = self.par[x];
            let r = self.find(p);
            self.diff_weight[x] += self.diff_weight[p];
            self.par[x] = r;
            r
        }
    }
    fn weight(&mut self,x:usize)->i64{
        self.find(x);
        self.diff_weight[x]
    }
    fn diff(&mut self, x:usize, y:usize)->i64{
        let res = self.weight(x) - self.weight(y);
        res
    }
    fn same(&mut self, a:usize, b:usize)->bool{
        self.find(a) == self.find(b)    
    }
    fn unite(&mut self, xx:usize, yy:usize, ww:i64) -> bool{
        let mut w = ww.clone();
        let mut x = xx.clone();
        let mut y = yy.clone();

        w += self.weight(x);
        w -= self.weight(y);
        x = self.find(x);
        y = self.find(y);
        if (x == y) {return false;}
        if self.rank[x] < self.rank[y]{
            mem::swap(&mut x, &mut y);
            w = -w;
        }

        if self.rank[x] == self.rank[y]{
            self.rank[y] += 1;
        }
        self.par[y] = x;
        self.size[x] += self.size[y];
        self.diff_weight[y] = w;
        return true;
    }
    fn check_size(&mut self, a:usize) -> usize{
        let x = self.find(a);
        let s = self.size[x];
        s    
    }
}





struct UnionFind{
    par:Vec<usize>,
    rank:Vec<usize>,
    size:Vec<usize>,    
}
impl UnionFind{
    fn init(n:usize) -> UnionFind{
        let mut par = vec![0;n];
        for i in 0..n{
            par[i] = i;    
        }
        UnionFind{
            par:par,
            rank:vec![0;n], 
            size:vec![1;n], 
        }
    }
    fn find(&mut self, x:usize) ->usize{
        if(self.par[x] == x){
            x    
        }
        else{
            let p = self.par[x];
            let res = self.find(p);
            self.par[x] = res;
            res
        }
    }
    fn same(&mut self, a:usize, b:usize)->bool{
        self.find(a) == self.find(b)    
    }
    fn unite(&mut self, a:usize, b:usize){
        let x = self.find(a);
        let y = self.find(b);
        if x != y{
            if (self.rank[x] < self.rank[y]){
                self.par[x] = y;
                self.size[y] += self.size[x];
            }
            else{
                self.par[y] = x;
                self.size[x] += self.size[y];
                if(self.rank[x] == self.rank[y]){ self.rank[x]+=1;}
            }
        }
    }
    fn check_size(&mut self, a:usize) -> usize{
        let x = self.find(a);
        let s = self.size[x];
        s    
    }
}
fn gcd(a:usize, b:usize)->usize{
    if b==0{return a;}
    gcd(b, a%b)
}
fn lcm(a: usize, b: usize) -> usize {
    a / gcd(a, b) * b
}
fn extgcd(a:usize, b:usize, x:&mut usize, y:&mut usize)->usize{
    let mut d = a;
    if b != 0{
        d = extgcd(b, a%b, y, x);
        *y -= (a/b) * (*x);    
    }    
    else{
        *x = 1;
        *y = 0;
    }
    d
}

use std::ops::{Deref, DerefMut, Index, IndexMut};
use std::any::{Any, TypeId};

struct vec2<T>(Vec<T>);
 
impl<T> Deref for vec2<T> {
    type Target = Vec<T>;
    fn deref(&self) -> &Vec<T> {
        &self.0
    }
}
 
impl<T> DerefMut for vec2<T> {
    fn deref_mut(&mut self) -> &mut Vec<T> {
        &mut self.0
    }
}
impl<T> Index<i64> for vec2<T> {
    type Output = T;
    fn index(&self, index: i64) -> &T {
        &self.0[index as usize]
    }
}
 
impl<T> IndexMut<i64> for vec2<T> {
    fn index_mut(&mut self, index: i64) -> &mut T {
        &mut self.0[index as usize]
    }
}

fn segment_sieve(a:usize, b:usize) -> Vec<bool>{
    let mut is_prime= vec![false; b+1];
    let mut is_prime_small= vec![false; b+1];
    for i in 0..b{
        if i*i>=b{break;}    
        is_prime_small[i] = true;
    }
    for i in 0..b{
        if i>=b-a{break;}
        is_prime[i] = true;    
    }
    for i in 2..b{
        if i*i>=b{break;}
        if is_prime_small[i] == true{


            let mut j = 2*i;
            while(j*j<b){
                is_prime_small[j] = false;
                j+=i;
            }
            
            j = cmp::max(2, (a+i-1)/i)*i;
            while(j<b){
                is_prime[j-a] = false;
                j+=i;    
            }    
        }    
    }
    is_prime


}

fn divisor(n:usize) -> Vec<usize>{
    let mut res:Vec<usize> = Vec::new(); 
    for i in 1..n+1{
        if i*i>n{break;}
        if n%i == 0{
            res.push(i);
            if i != n/i{
                res.push(n/i);    
            }    
        }    
    }
    res
}

fn prime_factor(nn:usize) -> HashMap<usize, usize>{
    let mut res:HashMap<usize, usize> = HashMap::new();
    let mut n = nn.clone();
    for i in 2..n+1{
        if i*i>n{break;}
        while(n%i == 0){
            *res.entry(i).or_insert(0) += 1;
            n/=i;    
        }    
    }
    if (n != 1){res.insert(n,1);}
    res
}

use std::collections::BinaryHeap;

#[derive(PartialEq)]
struct mf(i64);

impl Eq for mf {}

impl PartialOrd for mf {
    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl Ord for mf {
    fn cmp(&self, other: &mf) -> Ordering {
        self.partial_cmp(other).unwrap()
    }
}




#[derive(Copy, Clone, Eq, PartialEq)]
struct edge1{from:usize, to:usize, cost:i64}
impl Ord for edge1 {
    fn cmp(&self, other: &edge1) -> Ordering {
        other.cost.cmp(&self.cost)
    }
}

impl PartialOrd for edge1 {
    fn partial_cmp(&self, other: &edge1) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}
fn kruskal(es:&mut Vec<edge1>, n:usize) -> i64{
    es.sort();
    es.reverse();
    let mut uf =  UnionFind::init(n);
    let mut res = 0;
    for i in 0..es.len(){
        let e = es[i];
        if uf.same(e.from, e.to) == false{
            uf.unite(e.from, e.to);
            res += e.cost;
        }

    }
    res
}




fn bellman_ford(s:usize, n:usize, inf:i64, es:&Vec<edge1>) -> Vec<i64>{
    let mut d = vec![inf;n];
    d[s] = 0;
    for j in 0..n-1{
        let mut update = false;
        for i in 0..es.len(){
            let e = es[i];
            if (d[e.from] != inf && d[e.to] > d[e.from] + e.cost){
                d[e.to] = d[e.from] + e.cost;
            }
                
        }
    }

    d
}
fn find_negative_loop(n:usize, es:&Vec<edge1>, inf:i64) -> bool{
    let mut d = vec![0;n];
    for i in 0..n{
        for j in 0..es.len(){
            let e = es[j];
            if d[e.to] > d[e.from] + e.cost{
                d[e.to] = d[e.from] + e.cost;
                if (i == n-1) {return false;}
            }
        }
    }
    return true;
}
#[derive(Copy, Clone, Eq, PartialEq)]
struct State{
    cost: i64,
    position: usize,
}
impl Ord for State {
    fn cmp(&self, other: &State) -> Ordering {
        // Notice that the we flip the ordering on costs.
        // In case of a tie we compare positions - this step is necessary
        // to make implementations of `PartialEq` and `Ord` consistent.
        other.cost.cmp(&self.cost)
    }
}

// `PartialOrd` needs to be implemented as well.
impl PartialOrd for State {
    fn partial_cmp(&self, other: &State) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}

struct edge2{
    to:usize,
    cost:i64,
}
fn dijkstra(adj_list: &Vec<Vec<edge2>>, start:usize, inf:i64) -> Vec<i64>{
    let mut d= vec![inf;adj_list.len()];
    let mut heap = BinaryHeap::new();
    d[start] = 0;
    heap.push(State{cost: 0, position: start });
    while (heap.len() != 0){
        let p = heap.pop().unwrap();
        let v = p.position;
        if(d[v] < p.cost) {continue;}
        for i in 0..adj_list[v].len(){
            let e = &adj_list[v][i];
            if d[e.to] > d[v] + e.cost{
                d[e.to] = d[v] + e.cost;
                heap.push(State{cost:d[e.to], position:e.to});
            }
        }
            
    }
    d
        
}
// no verify
fn prim(n:usize, cost:&Vec<Vec<i64>>, inf:i64, s:usize) -> i64{
    let mut mincost = vec![inf;n];
    let mut used = vec![false;n];
    mincost[s] = 0;
    let mut res = 0;
    while(true){
        let mut v:i64 = -1;
        for  u in 0..n{
            if (used[u] == false && (v == -1 || mincost[u] <mincost[v as usize])){v = u.clone() as i64;}
        }
        if v == -1{break;}
        used[v as usize] = true;
        res += mincost[v as usize];
        for u in 0.. n{
            mincost[u] = cmp::min(mincost[u], cost[v as usize][u]);
        }
    }
    return res;
}
//
fn find_negative_loop2(n:usize, es:&Vec<edge1>, inf:i64, dist:&mut Vec<i64>) -> Vec<bool>{
    let mut neg = vec![false;n];
    for i in 0..n{
        for j in 0..es.len(){
            
            let e = es[j];
            if dist[e.from] == inf{continue;}

            if dist[e.to] > dist[e.from] + e.cost{
                dist[e.to] = dist[e.from] + e.cost;
                neg[e.to] = true;
            }
            if neg[e.from] == true{ neg[e.to] = true;}
        }
    }
    return neg;
}
fn main() {
    input!{
        n:usize,
        m:usize,
        xx:[(usize, usize, i64);m],
    }
    let mut es = Vec::new();
    for i in 0..m{
        es.push(edge1{from:xx[i].0 -1 , to:xx[i].1 - 1, cost:xx[i].2 * -1});
    }
    let inf = 20000000000000;
    let mut ans1 = bellman_ford(0, n, inf, &es);
    let res = ans1[n-1]*-1;
    let ans2= find_negative_loop2(n, &es, inf, &mut ans1);

    if ans2[n-1] == true{
        println!("inf");
    }
    else{
        println!("{}", res);
    }

}