A8909 | Slightly Decreasing Permutations

Permutation $p$ is an ordered set of integers $p_{1},p_{2},...,p_{n}$ , consisting of $n$ distinct positive integers, each of them doesn't exceed $n$ . We'll denote the $i$ -th element of permutation $p$ as $p_{i}$ . We'll call number $n$ the size or the length of permutation $p_{1},p_{2},...,p_{n}$ .

The decreasing coefficient of permutation $p_{1},p_{2},...,p_{n}$ is the number of such $i\ (1<=i<n)$ , that $p_{i}>p_{i+1}$ .

You have numbers $n$ and $k$ . Your task is to print the permutation of length $n$ with decreasing coefficient $k$ .

The single line contains two space-separated integers: $n,k\ (1<=n<=10^{5},0<=k<n)$ — the permutation length and the decreasing coefficient.

In a single line print $n$ space-separated integers: $p_{1},p_{2},...,p_{n}$ — the permutation of length $n$ with decreasing coefficient $k$ .

If there are several permutations that meet this condition, print any of them. It is guaranteed that the permutation with the sought parameters exists.