TEMPTISL - Temptation Island

On Monday, the number of frosh were reduced in half. To further reduce the number of engineers to a manageable number, the following challenge was devised for the second day. Each of the students would have to take this challenge individually.

Each student would be placed at a vertex of perimeter fence of Waterloo (oh yeah, some background: to keep UofT’s engineering Lady Godiva band out of Waterloo, a fence was erected surrounding the university. The fence just happens to be an N-gon). At some other vertex along the fence would be located a temptation so seductive that no Waterloo student could resist – an extra-credit assignment. The challenge of each student is to go from his starting vertex to the vertex with the prize. There are however 3 rules:

a) The student can only travel from vertex to vertex (backwards or forwards) along the polygonal fence.

b) The student has to make contact with exactly K vertices (the vertex he starts at doesn’t count unless he returns to it). The K vertices need not be unique. The final vertex has to be the one with the prize.

c) If the student cannot reach the prize and make contact with exactly K vertices, he fails the test and is kicked out of the university.

Of course, no Waterloo student is satisfied with only 1 solution to any problem. Therefore, inevitably, each student determines all ways that he/she can win. Note that there may be no solution to the problem (the astute student has figured out that this will result in a class size of 0 – this is entirely allowable as the variable used to quantify enrolment was incorrectly defined as a whole number instead of a natural number).

Input

N K (N, K <= 50)
A B (A = the starting vertex number, B = destination vertex number)
-1 -1 terminates input

Output

The total number of ways of reaching the destination from the starting point by following the above rules. The total number of ways will be less than 263 - 1. Output 0 if there are no solution.

Example

Input:
8 5
1 4
-1 -1

Output:
6

Added by:JaceTheMindSculptor
Date:2009-04-08
Time limit:0.5s-1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: C99 ERL JS-RHINO
Resource:Woburn Challenge 2001

hide comments
2011-11-01 21:48:05 যোবায়ের
1 based. doesn't matter whether n > 3 or not.
2011-06-05 15:56:00 jack(chakradarraju)
are the vertex numbers 0-based or 1-based?
Problem setter should make the problem statement more clear
2011-04-12 23:40:22 Santiago Palacio
Is there an input with n < 3?
2011-04-11 21:37:59 Santiago Palacio
Thanks sanky, i thought it was the incorrect way
2009-04-13 11:55:33 sanky
I add the info as I got confused.There are multiple sets where each set is
n1 k1
a1 b1
n2 k2
a2 b2
...
-1 -1(n and k) at the end.
It is not
n k
a1 b1
a2 b2
a3 b3
-1 -1(a and b)at the end.
2009-04-10 03:10:04 JaceTheMindSculptor
Output file had a mistake before. The problem statement used to say, "The total number of ways will be less than 2,147,483,647." (incorrect), instead of 2^63 - 1 (correct).

Last edit: 2009-04-10 03:20:54
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