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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 S_{1}S_{2} .. S_{N}, in the order in which they are placed inside the string. Such a string is called 'funny' if the string S_{1}+1S_{2}S_{3} .. S_{N-1}S_{N }-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 (S_{1}+S_{2}+..+S_{N}) is equal to K.

Input

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).

Output

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

Hint

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