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)

import           Control.Exception           (assert)
import           Control.Monad
import qualified Control.Monad.ST            as ST
import qualified Data.Array.IO               as IO
import qualified Data.Array.ST               as ST
import qualified Data.Array.Unboxed          as A
import           Data.Bits
import qualified Data.ByteString.Char8       as BS
import           Data.Char
import           Data.Foldable
import           Data.List
import           Data.Maybe
import qualified Data.Sequence               as Seq
import qualified Data.Set                    as Set
import qualified Data.Vector.Unboxed         as V
import qualified Data.Vector.Unboxed.Mutable as VM
import           Debug.Trace

readInt = fst . fromJust . BS.readInt
readIntList = map readInt . BS.words
getInt = readInt <$> BS.getLine
getIntList = readIntList <$> BS.getLine
getIntVec n = V.unfoldrN n (BS.readInt . BS.dropWhile isSpace) <$> BS.getLine

readInteger = fst . fromJust . BS.readInteger
readIntegerList = map readInteger . BS.words
getInteger = readInteger <$> BS.getLine
getIntegerList = readIntegerList <$> BS.getLine

type Edge = (Int, Int, Int)
eFrm  (frm, _, _)  = frm
eTo   (_, to, _)   = to
eCost (_, _, cost) = cost

shortestPath :: Int -> V.Vector (Int, Int, Int) -> Int
  -> IO (Maybe (V.Vector Int))
shortestPath s edges numV = do
  let numE = V.length edges
      inf = 10^18 :: Int

  d <- VM.new numV
  VM.set d inf
  VM.write d s 0

  let loop :: Int -> IO Bool
      loop i | i > numV = return True -- cyclic
             | otherwise = do update <- loop2 0 False
                              if update
                                then loop (i+1)
                                else return False

      loop2 :: Int -> Bool -> IO Bool
      loop2 j upd | j == V.length edges = return upd
                  | otherwise = do
                      let e = edges V.! j
                      d_frm <- VM.read d (eFrm e)
                      d_to  <- VM.read d (eTo e)
                      let ucond = d_frm /= inf && d_to > d_frm + eCost e
                          upd' = upd || ucond
                      when ucond $ VM.write d (eTo e) (d_frm + eCost e)
                      loop2 (j+1) upd'

  cyc <- loop 0
  res <- V.freeze d

  if cyc
    then return Nothing
    else return (Just res)

main = do
  [n, m] <- getIntList
  edges <- V.replicateM m $ do
    [a, b, c] <- getIntList
    return (a-1, b-1, (-c))

  maybe_costs <- shortestPath 0 edges n

  case maybe_costs of
    Nothing    -> putStrLn "inf"
    Just costs -> print ((-1) * (costs V.! (n-1)))