SCALE  Funny scales
Kinh_Can has a set of precious weights P_{1}, P_{2}, ..., P_{N} in which the mass of the i^{th} weight is P_{i} = 3^{i1}, and a balance with 2 scales. On a nice day, Kinh_Can decided to show off his set of precious weights to his friends, and said that he can put them in equilibrium with any weight as long as its mass is not more than the mass of the sum of his weights. At first, his friends didn't believe, but after many trials they realized that Kinh_Can was right. In addition, while putting a thing whose mass is X on a scale, Kinh_Can could put right away the weights added on the 2 scales to keep their blance without any trial. With a random weight X (X is a natural number, X ≠ 0). Your task is to put weights on scales in order to keep the 2 scales' balance like Kinh_Can. The first scale initially weights X, and the second one weights 0.
Input
Input has exactly one line consisting 2 numbers, the first is N and the second is X.
Output
 If there is no solution, you should write 1
 If there is at least one solution for the problem, you should write exactly 2 lines:
 The first line contains some numbers descripting the indices of the weights in the first disc
 The second line contains some numbers description the indices of the weights in the second disc
 Note: One of 2 lines can be blank
Constraints
 1 ≤ N ≤ 20
 1 ≤ X ≤ 2000000000
Example
Input 1: 10 2 Output 1: 1 2 Input 2: 10 5 Output 2: 1 2 3
hide comments
sieunhanbom04:
20160804 11:08:14
I think this problem is purely solved by mathematics (Ternary numeral system). 

Nic Roets:
20160309 18:39:19
It looks like some inputs contain more than one line. Continue reading until EOF or n < 1 or x < 1 

aghori_sadhu:
20151019 19:49:51
Try these cases :


Govind Lahoti:
20150227 22:03:13
Beautiful problem...


sriankit:
20130718 08:05:01
awsum... :) 

Trilok Sharma:
20130624 13:57:03
Best Test case is :


NodaR M JarraR:
20130421 16:23:09
i am getting wa in the 19th running ,, what should be the problem? i think that i solved it correctly!!


manish sharma:
20120418 13:48:10
can there be more than 1 solution 

cprocoder:
20110728 03:21:24
Very nice problem 

Sigma Kappa:
20110430 09:31:04
The numbers should be output in increasing order. 
Added by:  nha.duong 
Date:  20070729 
Time limit:  0.214s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  Classical 