Chase

Time Limit:	1000ms	Memory Limit:	64000KiB
Accepted:	0	Submitted:	0

Chase

POI V Stage 3 Problem 3

Chase

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:

it contains no triangles, i.e. there are no three distinct squares such that each pair of them is adjacent,
each square can be reached by each player.

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

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).

Sample Input

Sample Output

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