Niebieskie ksi.eczki
V Olimpiada Informatyczna 1997/1998
Task: GON
Author: Adam Borowski
Chase
III stage contest  

Chase is a two-person board game. A board consists of squares numbered from 1 to n. For each pair of different squares it is known if they are adjacent to one another or they are not. Each player has a piece at his disposal. At the beginning of a game pieces of players are placed on fixed, distinct squares. In one turn a player can leave his piece on the square it stands or move it to an adjacent square.

A game board has the following properties:

A game consists of many turns. In one turn each player makes a single move. Each turn is started by player A. We say that player A is caught by player B if both pieces stand on the same square. Decide, if for a given initial positions of pieces, player B can catch player A, independently of the moves of his opponent. If so, how many turns player B needs to catch player A if both play optimally (i.e. player A tries to run away as long as he can and player B tries to catch him as quickly as possible).

Example
[Example]

Consider the board in the figure. Adjacent squares (denoted by circles) are connected by edges. If at the beginning of a game pieces of players A and B stand on the squares 9 and 4 respectively, then player B can catch player A in the third turn (if both players move optimally). If game starts with pieces on the squares 8 (player A) and 4 (player B) then player B cannot catch player A (if A plays correctly).

Task

Write a program that:

  • reads from the text file GON.IN the description of a board and numbers of squares on which pieces are placed initially.
  • decides if player B can catch player A and if so, computes how many turns he needs (we assume that both players play optimally);
  • writes the result to the text file GON.OUT.

    Input

    In the first line of the input file GON.IN there are four integers n, m, a and b separated by single spaces, where 2<=n<=3000, n-1<=m<=15000, 1<=a,b<=n and a <b. These are (respectively): the number of squares of the board, the number of adjacent (unordered) pairs, the number of the square on which the piece of player A is placed, the number of the square on which the piece of player B is placed. In each of the following lines there are two distinct positive integers separated by a single space, which donote numbers of adjacent squares.

    Output

    In the first and only line of the file GON.OUT there should be:

  • one word NIE (which means NO in Polish), if player B can not catch player A, or
  • one integer - the number of turns needed by B to catch A (if B can catch A).

    Example

    For the input file GON.IN: 

    9 11 9 4
1 2
3 2
1 4
4 7
7 5
5 1
6 9
8 5
9 8
5 3
4 8
    the correct answer is the output file GON.OUT: 
    3