FJ's Sum Puzzle

FJ and his cows are playing an interesting mental game with numbers. Initially, the numbers from $1$ to $N$ (with $1 \le N \le 10$) are arranged in some order. Then, adjacent numbers are repeatedly summed to form a new list until only one number is left. Formally, if the initial sequence is $a_1, a_2, \dots, a_N$, then the final number is given by:

$$\text{Final} = \sum_{i=1}^{N} \binom{N-1}{i-1} a_i. $$

The cows now challenge FJ: given the final number and $N$, determine the original permutation of numbers $1, 2, \dots, N$ that produces the given final number. It is guaranteed that a unique solution exists.

inputFormat

The input consists of a single line containing two integers separated by a space: $N$ (the number of numbers) and $F$ (the final total after the summing process).

outputFormat

Output the unique permutation of numbers from $1$ to $N$ (separated by spaces) that produces the final sum $F$ when the described process is applied.

sample

4 16

3 1 2 4