Problem
E - Board Games

## Background

You have been hired by the quality
control division of a world famous board game company. Their creative and
design division comes up, on a daily basis, with great ideas for board games,
but sometimes the scoring of the proposed games does not match the storyboard
or leads the player to impossible or undesirable situations.

Most of the games this company produces
can be described loosely as race games. Race games are games where the players
need to go from an initial square to a final square, performing along the way,
a series of moves, gaining or losing score points for each of those moves.
Moves can be influenced by playerŐs decisions, drawing of cards, rolling of
dices, etc..

## Problem

Your task is to check the description of
a given game, stating the lowest possible score, or if it can lead to an
infinitely high (thereŐs no way the player can win the game), or to an
infinitely low score.

The input consists of one game
description. The first line of the input contains a positive integer **N **not greater than 300, indicating the number of squares in the game.
The second line contains two non-negative integers, **I** and **F**, defining the initial and
final squares for this game, where **I** and **F** are lesser than **N**. The third line
contains an integer **M**, indicating the number of
possible moves of the game. The following **M**
lines describe all the possible moves of the game. Each line, describing one
possible move, consists of three integers, respectively, the initial square and
final square of the move, in the range **[0, N-1]**,
and the corresponding score.

The output consists of a single line with
an integer, indicating the lowest possible score for the proposed game. If the
scores are infinitely high or low then your program should output **infinity**.

4

0 3

4

0 1 5

0 2 7

2 1 -3

1 3 2

6

4

0 3

3

0 1 5

0 2 7

2 1 -3

infinity