|Codeforces Round #375 (Div. 2)|
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 ≤ 109), 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.
1 2 3 2
1 2 1 2
1 3 2 2 2 2 1
1 3 3 2 2 2 1
1000000000 100 7 1000000000
1 2 3 4
In the first sample, after Polycarp's changes the first band performs two songs ( b 1 = 2), and the second band also performs two songs ( b 2 = 2). Thus, the minimum of these values equals to 2. It is impossible to achieve a higher minimum value by any changes in the playlist.
In the second sample, after Polycarp's changes the first band performs two songs ( b 1 = 2), the second band performs three songs ( b 2 = 3), and the third band also performs two songs ( b 3 = 2). Thus, the best minimum value is 2.