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137. Funny Strings

time limit per test: 0.25 sec.
memory limit per test: 4096 KB

Let's consider a string of non-negative integers, containing N elements. Suppose these elements are S1 S2 .. SN, in the order in which they are placed inside the string. Such a string is called 'funny' if the string S1+1 S2 S3 .. SN-1 SN -1 can be obtained by rotating the first string (to the left or to the right) several times. For instance, the strings 2 2 2 3 and 1 2 1 2 2 are funny, but the string 1 2 1 2 is not. Your task is to find a funny string having N elements, for which the sum of its elements (S1+S2+..+SN) is equal to K.


The input contains two integers: N (2<=N<=1000) and K (1<=K<=30000). Moreover, GCD(N,K)=1 (it can be proven that this is a necessary condition for a string to be funny).


You should output one line containing the elements of the funny string found. These integers should be separated by blanks.


GCD(A,B) = the greatest common divisor of A and B.
The 'funny' strings are also named Euclid strings in several papers.

Sample Input

9 16

Sample Output

1 2 2 2 1 2 2 2 2

Author: Mugurel Ionut Andreica
Resource: SSU::Online Contester Fall Contest #2
Date: Fall 2002