A10630 | Polycarp at the Radio

Polycarp is a music editor at the radio station. He received a playlist for tomorrow, that can be represented as a sequence $a_{1},a_{2},...,a_{n}$ , where $a_{i}$ is a band, which performs the $i$ -th song. Polycarp likes bands with the numbers from $1$ to $m$ , but he doesn't really like others.

We define as $b_{j}$ the number of songs the group $j$ is going to perform tomorrow. Polycarp wants to change the playlist in such a way that the minimum among the numbers $b_{1},b_{2},...,b_{m}$ will be as large as possible.

Find this maximum possible value of the minimum among the $b_{j}$ ( $1<=j<=m$ ), and the minimum number of changes in the playlist Polycarp needs to make to achieve it. One change in the playlist is a replacement of the performer of the $i$ -th song with any other group.

The first line of the input contains two integers $n$ and $m$ ( $1<=m<=n<=2000$ ).

The second line contains $n$ integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ), where $a_{i}$ is the performer of the $i$ -th song.

In the first line print two integers: the maximum possible value of the minimum among the $b_{j}$ ( $1<=j<=m$ ), where $b_{j}$ is the number of songs in the changed playlist performed by the $j$ -th band, and the minimum number of changes in the playlist Polycarp needs to make.

In the second line print the changed playlist.

If there are multiple answers, print any of them.