F. The Lazy Author
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Since the author of this problem is too lazy to write a problem statement, he will provide you with the problem sketch only.

You're given an array $$$a$$$ of length $$$n$$$ consisting of zeros and ones, and an integer $$$k$$$.

You can perform no more than $$$n$$$ operations. In one operation, you take a range of length exactly $$$k$$$ and flip its values, making every $$$0$$$ a $$$1$$$ and every $$$1$$$ a $$$0$$$.

More formally, in each operation you can choose a value $$$l$$$ ($$$1 \le l \le n-k+1$$$) then do the assignment $$$a_i := 1-a_i$$$ for every $$$i$$$ such that $$$l \le i \le l+k-1$$$

Your task is to modify the array so that it contains no more than $$$\lfloor\frac{k}{2}\rfloor$$$ zeros.

Print the sequence of operations. If there are multiple answers, print any.

Input

The first line contains two integers, $$$n$$$ and $$$k$$$, where $$$(1 \leq k \leq n \leq 10^6)$$$.

The second line contains $$$n$$$ integers, $$$a_i$$$, where $$$(0 \leq a_i \leq 1)$$$.

Output

The first line contains a number, $$$m$$$, which represents the number of operations.

The second line contains $$$m$$$ integers, which represent the left side of each range.

If there are multiple answers, you can print any.

Examples
Input
3 2
1 0 1
Output
0
Input
4 2
0 0 0 0
Output
2
1 3
Note

in the first test you don't need to do any operations.

in the second test you can just do operations in [1,2] and [3,4].