In the middle of winter, djq and dxm are playing cards.

The two players first agree on two positive integers $n$ and $k$, such that $n$ is even and $n \geq 2k$. Then, each player receives $k$ cards. The $i$-th card ($1 \leq i \leq k$) in dxm's hand has the positive integer $n+(2i-1)$ written on it, and the $i$-th card in djq's hand has the positive integer $n-(2i-1)$ written on it. Note that the cards held by both players together form $2k$ consecutive odd integers.

The game consists of $k$ rounds. In each round, both players play one card from their remaining hand, and played cards cannot be retrieved. If the numbers on the two cards are coprime, djq scores one point; otherwise, dxm scores one point. After all rounds are completed, both players calculate their total scores.

djq already knows that in the $i$-th round, dxm will play the $i$-th card from his hand. Now he wants to know:

• His highest possible score;
• A strategy for playing his cards to achieve this maximum score.

Please write a program to help him!

Input

A single line containing two positive integers $n$ and $k$.

Output

The first line should output an integer $s$, representing the maximum possible score for djq.

The next $k$ lines should each output an integer, where the $i$-th line contains the integer $p_i$, representing the index of the card djq should play in the $i$-th round.

Examples

Input 1

10 3

Output 1

3
3
1
2

Note 1

dxm's cards are $[11, 13, 15]$ in order, and djq's cards are $[9, 7, 5]$ in order. djq only needs to play his cards in the order $[5, 9, 7]$ to get all $3$ points.

Implementation Details

This problem uses a Special Judge. To ensure the Special Judge works correctly, you must ensure:

• The first line of your output is an integer in $[0, k]$.
• The next $k$ lines each contain an integer in $[1, k]$.
• The output contains no other content.

Violating these specifications may result in receiving no points.

Provided the output follows the specifications, scoring is as follows:

• If both $s$ and the output strategy are correct, you receive full marks for the test case.
• If $s$ is correct but the output strategy is incorrect, you receive $15\%$ of the marks for the test case.
• Otherwise, you will receive no marks.

Constraints

For all data, $1 \leq k \leq 10^6$, $2k \leq n \leq 10^{100}$, and $n$ is guaranteed to be even.

This problem consists of several subtasks. For each subtask, your score is the minimum score among all test cases within that subtask.