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: Wrong Answer)

{-# LANGUAGE FlexibleContexts #-}

import Control.Monad
import Control.Monad.ST
import Control.Applicative
import Data.List
import Data.Array
import Data.Array.ST
import Data.Maybe
import Data.Bits
import Data.Ord
import Data.Ratio
import Data.Int
import Data.Char
import qualified Data.ByteString.Char8 as BS
import qualified Data.Set as Set
import Data.STRef
import Text.Printf
import Debug.Trace
import Numeric

modifyArray arr i f = readArray arr i >>= \x -> writeArray arr i (f x)

listToTuple2 [a,b] = (a,b)
listToTuple3 [a,b,c] = (a,b,c)
listToTuple4 [a,b,c,d] = (a,b,c,d)

getWords = getLine >>= return . words

readIntBS = fst . fromJust . BS.readInt

for = flip map


main :: IO ()
main = do
  (n,m) <- listToTuple2 . map read . words <$> getLine :: IO (Int,Int)
  edges <- map ((\(a,b,c) -> (read a, read b, read c)) . listToTuple3 . words) . lines <$> getContents :: IO [(Int,Int,Int64)]

  let a = negate $ bellman_ford (1,n) (map (\(a,b,c) -> (a,b,-c)) edges) 1 n

  putStrLn $ if a == inf then "inf" else show a
  


inf = 10^10 :: Int64

type Node = Int
type Cost = Int64
type Edge = (Node, Node, Cost)

bellman_ford :: (Node,Node) -> [Edge] -> Node -> Node -> Cost
bellman_ford bound@(lower,upper) edges src dst = runST $ do
  arr <- newArray bound inf :: ST s (STUArray s Node Cost)
  negcycle <- newSTRef False :: ST s (STRef s Bool)

  writeArray arr src 0
  forM_ [1..(upper-lower+1)] $ \i -> do
    forM_ edges $ \(s,e,c) -> do
      x <- (+c) <$> readArray arr s
      y <- readArray arr e
      when (x < y) $ do
        writeArray arr e x
          
  forM_ [1..(upper-lower+1)] $ \i -> do
    forM_ edges $ \(s,e,c) -> do
      x <- (+c) <$> readArray arr s
      y <- readArray arr e
      when (x < y) $ do
        writeArray arr e x
        when (e == dst) $ do
          writeSTRef negcycle True

  ncExists <- readSTRef negcycle
  if ncExists then
    return (-inf)
    else
    readArray arr dst