Codeforces Round #375 (Div. 2) C

Description

 

Polycarp is a music editor at the radio station. He received a playlist for tomorrow, that can be represented as a sequence a1, a2, ..., an, where ai 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 bj 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 b1, b2, ..., bm will be as large as possible.

Find this maximum possible value of the minimum among the bj (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.

Input

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

The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109), where ai is the performer of the i-th song.

Output

In the first line print two integers: the maximum possible value of the minimum among the bj (1 ≤ j ≤ m), where bj 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.

Examples

input

4 2
1 2 3 2

output

2 1
1 2 1 2 

input

7 3
1 3 2 2 2 2 1

output

2 1
1 3 3 2 2 2 1 

input

4 4
1000000000 100 7 1000000000

output

1 4
1 2 3 4 

Note

In the first sample, after Polycarp's changes the first band performs two songs (b1 = 2), and the second band also performs two songs (b2 = 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 (b1 = 2), the second band performs three songs (b2 = 3), and the third band also performs two songs (b3 = 2). Thus, the best minimum value is 2.

题意：n首歌曲，a_i 表示唱歌的乐队，题目主角喜欢1 2 ..M的乐队，希望歌单全是他们唱的，并且要求唱歌最少的乐队唱的歌的数目也是最小值中最大的（举个列子，5可以分为1 4,2 3，2是最小中的最大值）

解法：当然是平分啦，ans=n/m，那么我们遍历1到M，如果b_i乐队（乐队小于M）唱的歌小于ans,从a数组不符合要求的元素(比如a_i乐队唱的歌大于ans或者a_i乐队大于M)中拿，处理一下拿走的元素就行

#include<stdio.h>
//#include<bits/stdc++.h>
#include<string.h>
#include<iostream>
#include<math.h>
#include<sstream>
#include<set>
#include<queue>
#include<map>
#include<vector>
#include<algorithm>
#include<limits.h>
#define inf 0x3fffffff
#define INF 0x3f3f3f3f
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define LL long long
#define ULL unsigned long long
using namespace std;

int a[100000];
map<int,int>q;
int num=0;
int main()
{
    int n,m;
    int ans;
    cin>>n>>m;
    ans=n/m;
    for(int i=0;i<n;i++)
    {
        cin>>a[i];
        q[a[i]]++;
    }
    num=0;
    for(int i=1;i<=m;i++)
    {
        if(q[i]<ans)
        {
            while(q[i]<ans)
            {
                for(int j=0;j<n;j++)
                {
                   // cout<<i<<"A"<<endl;
                    if(a[j]>m||q[a[j]]>ans)
                    {
                      //  cout<<i<<" "<<a[j]<<endl;
                        q[a[j]]--;
                        q[i]++;
                        a[j]=i;
                        num++;
                        break;
                    }
                }
            }
        }
    }
    cout<<ans<<" "<<num<<endl;
    for(int i=0;i<n;i++)
    {
        cout<<a[i]<<" ";
    }
    return 0;
}

　　

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