CF513B1 Permutations

You are given a permutation $ p $ of numbers $ 1,2,...,n $ . Let's define $ f(p) $ as the following sum: Find the lexicographically $ m $ -th permutation of length $ n $ in the set of permutations having the maximum possible value of $ f(p) $ .

The single line of input contains two integers $ n $ and $ m $ ( $ 1

Output $ n $ number forming the required permutation.

In the first example, both permutations of numbers {1, 2} yield maximum possible $ f(p) $ which is equal to 4. Among them, $ (2,1) $ comes second in lexicographical order.