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 OCaml (4.02.3) (judge verdict: Accepted)

module WeightedDirectedGraph
  (Weight : sig
    type t
    val inf : t
    val zero : t
    val neg_inf : t
    val ( + ) : t -> t -> t
    val compare : t -> t -> int
  end) :
sig
  type 'a church_list = { fold : 'b. ('a -> 'b -> 'b) -> 'b -> 'b }

  val bellman_ford :
    (* 頂点数n *)
    int ->
    (* 辺のリスト
       頂点は0からn-1までの整数でなくてはならない
       2n回呼び出されるので，リストを作るのに時間がかかるならメモ化すること *)
    (int * int * Weight.t) church_list ->
    (* 始点 *)
    int ->
    (* 頂点を受け取り，そこまでの距離を返す関数
       頂点に到達するパスが無ければinfを返し，
       そこに到達するまでに負閉路があればneg_infを返す *)
    (int -> Weight.t)
end =
struct
  type 'a church_list = { fold : 'b. ('a -> 'b -> 'b) -> 'b -> 'b }

  let bellman_ford n es s =
    (* 距離を覚えるやつ *)
    let d = Array.make n Weight.inf in
    (* 経路に負閉路が含まれる頂点を覚えるやつ *)
    let neg = Array.make n false in
    d.(s) <- Weight.zero;
    (* n回目以降の反復 手動ループアンローリング *)
    let rec loop' n =
      if
        0 < n &&
        es.fold (fun (u, v, c) b -> (* bは更新の有無 *)
          let open Weight in
          (* c は u から v への辺の重さ
             d.(u) + c < d.(v) *)
          0 < Weight.compare d.(v) (d.(u) + c)
          (* n 回目以降に変更が起こった場合，v までの経路に負閉路が含まれている *)
          && (d.(v) <- d.(u) + c; neg.(v) <- true; true) || b) false
      then loop' (n - 1) in
    (* n-1回目までの反復 *)
    let rec loop = function
      | 0 -> loop' n
      | n ->
          if
            es.fold (fun (u, v, c) b ->
              let open Weight in
              0 < Weight.compare d.(v) (d.(u) + c) && (d.(v) <- d.(u) + c; true) || b) false
          then loop (n - 1) in
    loop (n - 1);
    fun v -> if neg.(v) then Weight.neg_inf else d.(v)
end

module G = WeightedDirectedGraph (struct
  type t = int
  let inf = -123456789012345678
  let zero = 0
  let neg_inf = 123456789012345678
  let ( + ) = ( + )
  let compare x y = compare y x
end)

let () = Scanf.scanf "%d %d\n" @@ fun n m ->
  let abcs = Array.init m @@ fun _ -> Scanf.scanf "%d %d %d\n" @@ fun a b c -> a - 1, b - 1, c in
  let d = G.bellman_ford n { G.fold = fun f -> Array.fold_right f abcs } 0 (n - 1) in
  if 123456789012345678 <= d
  then print_endline "inf"
  else Printf.printf "%d\n" d