Polycarp at the Radio

题意翻译

有n个数，用最少的次数来改变数字，使得1到m出现的次数的最小值最大。输出最小值和改变次数以及改变后的数组。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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.

输入输出样例

输入样例 #1

4 2
1 2 3 2

输出样例 #1

2 1
1 2 1 2 

输入样例 #2

7 3
1 3 2 2 2 2 1

输出样例 #2

2 1
1 3 3 2 2 2 1 

输入样例 #3

4 4
1000000000 100 7 1000000000

输出样例 #3

1 4
1 2 3 4 

说明

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 $ .