Max or Min

Kevin has $n$ integers $a_1, a_2, \ldots, a_n$ arranged in a circle. That is, $a_i$ and $a_{i+1}$ ($1 \le i < n$) are neighbors, and $a_1$ and $a_n$ are neighbors as well. Therefore, each number has exactly two neighbors.

In one minute, Kevin can set $a_i$ to the minimum among the three numbers $a_i$ and its two neighbors. Alternatively, he can set $a_i$ to the maximum among the same three numbers. For example, if $a_i = 5$ and its two neighbors are 3 and 2, and Kevin performs the minimum operation, $a_i$ becomes 2. If he performs the maximum operation, however, $a_i$ stays 5.

For each $x$ from 1 to $m$, find the minimum number of minutes needed to make all numbers equal $x$, or determine that it is impossible.

The first line contains two integers $n$ and $m$ ($3 \le n \le 2 \cdot 10^5$, $1 \le m \le 2 \cdot 10^5$): the number of integers in the circle and the number of values you need answers for.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le m$).

Print $m$ integers. The $i$-th integer is the minimum number of minutes needed to make all numbers equal $i$, or $-1$ if it is impossible.

To make all numbers equal 2, Kevin needs at least 5 minutes. One possible sequence of operations:

1. Apply the minimum operation to $a_6$. It becomes 2.
2. Apply the maximum operation to $a_4$. It becomes 2.
3. Apply the maximum operation to $a_3$. It becomes 5.
4. Apply the minimum operation to $a_2$. It becomes 2.
5. Apply the minimum operation to $a_3$. It becomes 2.