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Posted 2022-12-25 yy666

One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of $$$n$$$ non-negative integers.

If there are exactly $$$K$$$ distinct values in the array, then we need $$$k = \lceil \log_2 K \rceil$$$ bits to store each value. It then takes $$$nk$$$ bits to store the whole file.

To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers $$$l \le r$$$, and after that all intensity values are changed in the following way: if the intensity value is within the range $$$[l;r]$$$, we don‘t change it. If it is less than $$$l$$$, we change it to $$$l$$$; if it is greater than $$$r$$$, we change it to $$$r$$$. You can see that we lose some low and some high intensities.

Your task is to apply this compression in such a way that the file fits onto a disk of size $$$I$$$ bytes, and the number of changed elements in the array is minimal possible.

We remind you that $$$1$$$ byte contains $$$8$$$ bits.

$$$k = \lceil log_2 K \rceil$$$ is the smallest integer such that $$$K \le 2^k$$$. In particular, if $$$K = 1$$$, then $$$k = 0$$$.

    <dt>Input</dt>
    <dd><p>The first line contains two integers $$$n$$$ and $$$I$$$ ($$$1 \le n \le 4 \cdot 10^5$$$, $$$1 \le I \le 10^8$$$)&nbsp;— the length of the array and the size of the disk in bytes, respectively.</p>

The next line contains $$$n$$$ integers $$$a_i$$$ ($$$0 \le a_i \le 10^9$$$) — the array denoting the sound file.

    <dt>Output</dt>
    <dd><p>Print a single integer&nbsp;— the minimal possible number of changed elements.</p></dd>

    <dt>Examples</dt>
    <dd><div class="sample-test">

Input

6 1

2 1 2 3 4 3

Output

2

Input

6 2

2 1 2 3 4 3

Output

0

Input

6 1

1 1 2 2 3 3

Output

2