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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

{-# LANGUAGE FlexibleContexts #-}

import Control.Monad
import Data.STRef
import Data.Array
import Data.Array.ST
import Control.Monad.ST

data Score = Inf | Fin !Int deriving (Eq,Show)
instance Ord Score where
  compare Inf     Inf = EQ
  compare (Fin _) Inf = LT
  compare Inf (Fin _) = GT
  compare (Fin a) (Fin b)= compare a b

plus::Score -> Score -> Score
plus Inf _ = Inf
plus _ Inf = Inf
plus (Fin a) (Fin b) = Fin (a+b)

--type W_D_graph = Array (Int,Int) Score
--graph implimentation changed: (a,b,c):a to b wieght c
type Graph = [(Int,Int,Int)]

bellman_ford::Graph -> Int -> Int -> Array Int (Maybe Score)
bellman_ford gr size st = runST $ do
  tab<- newArray (1,size) (Inf,True)
  writeArray tab st (Fin 0,True)
  tab_ptr<-newSTRef tab
  forM_ [1..(size-1)]$(propagate True  gr tab_ptr)
  forM_ [1..size    ]$(propagate False gr tab_ptr)
  ar<-freeze tab
  let result =listArray (1,size) $(map (\(x,b)->if b then Just x else Nothing) (elems ar))
  return result

propagate::Bool -> Graph ->STRef s (STArray s Int (Score,Bool))  -> Int -> (ST s ())
propagate flag gr tab_ptr _= do
  forM_ gr (one_edge_update)
        where one_edge_update (a,b,c) = do
                              tab<-readSTRef tab_ptr
                              tab_a<-readArray tab a
                              tab_b<-readArray tab b
                              let next_b = min (plus (fst(tab_a)) (Fin (-c))) (fst(tab_b))
                              let next_flag = (next_b == (fst(tab_b)))
                              writeArray tab b (next_b, (flag||next_flag) )




n_get::Int ->IO [(Int,Int,Int)]
n_get 0 =return []
n_get n =do
  d<-getLine
  let a:b:w:[]= map read (words d)
  rest <- n_get (n-1)
  return ((a,b,w):rest)

main::IO()
main=do
  nmc<-getLine
  let n:m:[]=map read (words nmc)::[Int]
  gr<-n_get m
  let ans = (bellman_ford gr n 1)!n
  case ans of
    Nothing -> do putStr ("inf"++"\n")
    Just (Fin x) -> do print (-x)