Given two integers $n$ and $k$, your task is to construct an array that contains every integer between $1 \dots n$ exactly once and there are exactly $k$ consecutive elements such that the first element is greater than the second element.

Input

The only input line has two integers $n$ and $k$.

Output

Print one line that contains the array. You may print any valid solution.

Constraints

• $0 \le k < n \le 10^5$

Example

Input:

5 2

Output:

1 4 2 5 3