C. Egg Order
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Eggo has $$$n$$$ eggs, one of each size from $$$1$$$ to $$$n$$$. He wants to figure out what order to place the eggs. A powerful subarray is one where each element is one size greater than the previous. More formally, if $$$b_1, b_2, \dots, b_k$$$ are the sizes of the eggs in the subarray, then the subarray is powerful if $$$b_i - b_{i - 1} = 1$$$ for $$$2 \leq i \leq k$$$. The power of a configuration of eggs is the size of the largest powerful subarray.

You want the power of the configuration to exactly equal $$$k$$$. Can you place the eggs such that the power equal $$$k$$$? If multiple answers exist, print any.

An array $$$b$$$ is a subarray of an array $$$a$$$ if $$$b$$$ can be obtained from $$$a$$$ by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. Note that an array is a subarray of itself.

Input

The first and only line of input consists of two integers $$$n$$$ and $$$k$$$ ($$$1 \leq k \leq n \leq 2 \cdot 10^5$$$) — the number of eggs and the desired power, respectively.

Output

Print $$$n$$$ space-separated integers $$$a_1, a_2, \dots, a_n$$$ — the order of eggs that gives the desired power.

Example
Input
5 3
Output
5 2 3 4 1