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. 

import java.util.*;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author flk
 */
public class main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }
}

/*class TaskA {

    public void solve(int testNumber, Scanner in, PrintWriter out) {

        int x1 = in.nextInt();
        int x2 = in.nextInt();
        int x3 = in.nextInt();

        int max = Math.max(Math.max(x1, x2), x3);
        int min = Math.min(Math.min(x1, x2), x3);

        out.print(max-min);
    }

}*/

/*
class TaskB {

    public void solve(int testNumber, Scanner in, PrintWriter out) {

        int n = in.nextInt(); in.nextLine();

        String s = in.nextLine();

        boolean inParen = false;
        int longestWordOut = 0;
        int numWordsIn = 0;
        int currWordLength = 0;

        for (int i = 0; i < s.length(); i++) {
            char c = s.charAt(i);

            if (c == '_' || c == '(' || c == ')') {
                // save word
                if (currWordLength > 0) {
                    if (inParen) {
                        numWordsIn++;
                    }
                    else {
                        if (currWordLength > longestWordOut) {
                            longestWordOut = currWordLength;
                        }
                    }
                    currWordLength = 0;
                }

                // revise position
                if (c == '(') inParen = true;
                if (c == ')') inParen = false;
            }
            else {
                currWordLength++;
            }
        }

        if (currWordLength > longestWordOut) {
            longestWordOut = currWordLength;
        }

        out.print(String.valueOf(longestWordOut) + ' ' + String.valueOf(numWordsIn));
    }

}*/

class TaskC {

    public boolean check(int mid, int[] b, int m) {
        int[] bcopy = Arrays.copyOf(b, b.length);

        //try m
        for (int i = 1; i <= m; i++) {
            while (bcopy[i] < mid) {
                //find conversions
                if (bcopy[0] > 0) {
                    bcopy[0]--;
                    bcopy[i]++;
                } else {
                    boolean done = false;
                    for (int j = 1; j <= m && !done; j++) {
                        if (bcopy[j] > mid) {
                            bcopy[j]--;
                            bcopy[i]++;
                            done = true;
                        }
                    }
                    if (!done) return false;
                }
            }
        }

        return true;
    }

    public void solve(int testNumber, Scanner in, PrintWriter out) {

        int n = in.nextInt();
        int m = in.nextInt();
        in.nextLine();

        int a[] = new int[n];
        int b[] = new int[m + 1];

        ArrayList<ArrayList<Integer>> mtoa = new ArrayList<ArrayList<Integer>>();
        for (int i = 0; i <= m; i++) {
            ArrayList<Integer> al = new ArrayList<Integer>();
            mtoa.add(al);
        }

        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();

            if (a[i] > m) {
                b[0]++;
                mtoa.get(0).add(i);
            } else {
                b[a[i]]++;
                mtoa.get(a[i]).add(i);
            }

        }

        // greedy?
        int L = 0;
        int R = 2046;
        boolean notFound = true;
        int mid = 10;

        int maxSuccess = 0;

        bigLoop:
        while (mid != L && mid != R) {
            mid = (L + R) / 2;

            if (!check(mid, b, m)) {
                R = mid; mid--;
            }
            else {
                if (mid > maxSuccess) maxSuccess = mid;
                //L = mid + 1;
                L = mid; mid++;
            }
        }

        //try one higher
        if (check(maxSuccess+1,b,m)) maxSuccess++;

        //final check
        int[] bcopy = Arrays.copyOf(b, b.length);
        int numChanges = 0;
        nextLoop2:
        for (int i = 1; i <= m; i++) {
            while (bcopy[i] < maxSuccess) {
                //find conversions
                if (bcopy[0] > 0) {
                    bcopy[0]--;
                    bcopy[i]++;
                    numChanges++;
                    int temp = mtoa.get(0).remove(mtoa.get(0).size()-1);
                    a[temp] = i;
                } else {
                    boolean done = false;
                    for (int j = 1; j <= m && !done; j++) {
                        if (bcopy[j] > maxSuccess) {
                            bcopy[j]--;
                            bcopy[i]++;
                            numChanges++;
                            done = true;
                            int temp = mtoa.get(j).remove(mtoa.get(j).size()-1);
                            a[temp] = i;
                        }
                    }
                    if (!done) {
                        //can't
                        //mid--;
                        out.println("Fail");
                        break nextLoop2;

                    }
                }
            }
        }

        out.println(String.valueOf(maxSuccess) + ' ' + String.valueOf(numChanges));
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < a.length; i++) {
            sb.append(String.valueOf(a[i]));
            sb.append(" ");
        }
        out.println(sb);
    }

}
/*
class TaskD {

    public class UnionFind {

        private int[] _parent;
        private int[] _rank;


        public int find(int i) {

            int p = _parent[i];
            if (i == p) {
                return i;
            }
            return _parent[i] = find(p);

        }


        public void union(int i, int j) {

            int root1 = find(i);
            int root2 = find(j);

            if (root2 == root1) return;

            if (_rank[root1] > _rank[root2]) {
                _parent[root2] = root1;
            } else if (_rank[root2] > _rank[root1]) {
                _parent[root1] = root2;
            } else {
                _parent[root2] = root1;
                _rank[root1]++;
            }
        }


        public UnionFind(int max) {

            _parent = new int[max];
            _rank = new int[max];

            for (int i = 0; i < max; i++) {
                _parent[i] = i;
            }
        }

    }


    public void solve(int testNumber, Scanner in, PrintWriter out) {

        int n = in.nextInt();
        int m = in.nextInt();
        int k = in.nextInt();
        in.nextLine();

        boolean[][] map = new boolean[n][m];

        for (int i = 0; i < n; i++) {
            String s = in.nextLine();
            for (int j = 0; j < m; j++) {
                map[i][j] = (s.charAt(j) == '.');
            }

        }

        UnionFind uf = new UnionFind(n*m+1);
//        uf.union(1,2);

//        int lakeNum
  //      int[][] lakes = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (map[i][j]) { // water {
                    if (i+1 < n && map[i+1][j]) uf.union(i*m+j,(i+1)*m+j);
                    //if (i+1 < n && j+1 < m && map[i+1][j+1]) uf.union(i*m+j,(i+1)*m+(j+1));
                    if (j+1 < m && map[i][j+1]) uf.union(i*m+j,(i)*m+(j+1));
                    //if (j+1 < m && i-1>0 && map[i-1][j+1]) uf.union(i*m+j,(i-1)*m+(j+1));
                }
                else uf.union(i*m+j,m*n);
            }
        }

        // get rid of ocean lakes
        for (int i = 0; i < n; i++) {

            //j 0
            uf.union(i*m+0,m*n);

            // j m-1
            uf.union(i*m+(m-1),m*n);

        }
        for (int j = 0; j < m; j++) {

            //i 0
            uf.union(0*m+j,m*n);

            // i n-1
            uf.union((n-1)*m+j,m*n);

        }



        int[] lakes = new int[n*m+2];


        //find lakes
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                lakes[uf.find(i*m+j)]++;
            }
        }
        // find land and remove
        lakes[uf.find(m*n)] = 0;


        HashMap<Integer, Integer> hm = new HashMap<Integer,Integer>();

        int numLakes = 0;
        int sumLand = 0;
        for (int i = 0; i < lakes.length; i++) {
            sumLand += lakes[i];
            if (lakes[i] > 0) {
                numLakes++;
                hm.put(i,lakes[i]);
            }
        }

        List<Map.Entry<Integer, Integer>> l = new ArrayList<Map.Entry<Integer, Integer>>(hm.entrySet());

        Collections.sort(l, new Comparator<Map.Entry<?, Integer>>() {
            @Override
            public int compare(Map.Entry<?, Integer> e1, Map.Entry<?, Integer> e2) {
                return e2.getValue().compareTo(e1.getValue());
            }
        });

        int Fills = 0;
        // fill lakes smallest to largest
        for (int o = 0; o < l.size()-k; o++) {
            int ent = l.get(l.size()-1-o).getKey();
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    if (uf.find(i*m+j) == ent) {
                        map[i][j] = false;
                        Fills++;
                    }
                }
            }

        }

        out.println(String.valueOf(Fills));
        for (int i = 0; i < n; i++) {
            String s = "";
            for (int j = 0; j < m; j++) {
                if (map[i][j]) s = s+".";
                else s = s+"*";
            }
            out.println(s);
        }
    }

}*/

