L. Not the Longest Increasing Subsequence
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

There is an array of $$$n$$$ integers. Each element $$$a_i$$$ in this array is between $$$1$$$ and $$$k$$$.

What is the smallest number of elements that should be removed from this array, so that its longest increasing subsequence has length smaller than $$$k$$$?

Input

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 10^6, 1 \le k \le n$$$) — the length of the array and the upper bound for its elements.

The second line contains $$$n$$$ integers $$$a_i$$$ ($$$1 \le a_i \le k$$$) — the elements of the array.

Output

In the first line output an integer $$$m$$$ — the number of elements to remove.

In the second line output $$$m$$$ integers — the indices of the removed elements. The indices are numbered from $$$1$$$ to $$$n$$$.

Examples
Input
3 2
1 2 2
Output
1
1
Input
2 2
2 1
Output
0
Input
8 3
1 2 2 1 1 3 2 3
Output
2
1 7