Given 2 integers ~N~ and ~K~, find the lexicographically largest permutation of ~1, 2, 3 \ldots N~ such that it takes exactly ~K~ swaps (between any two elements) to most efficiently sort it.
We define the most efficient sorting of an array of integers as one where the number of swaps is minimized.
The answer is guaranteed to exist.
The first and only line will contain ~2~ integers, ~N\: (1 \leq N \leq 10^6),\:K\:(0 \leq K \leq 10^6)~.
On one line, output the lexicographically greatest array that satisfies the conditions outlined in the problem statement.
Sample Input 1
Sample Output 1
4 3 1 2