You are given an array consisting of n integers a_1, a_2, ..., a_n, and a positive integer m. It is guaranteed that m is a divisor of n.

In a single move, you can choose any position i between 1 and n and increase a_i by 1.

Let's calculate c_r (0 ≤ r ≤ m-1) — the number of elements having remainder r when divided by m. In other words, for each remainder, let's find the number of corresponding elements in a with that remainder.

Your task is to change the array in such a way that c_0 = c_1 = ... = c_{m-1} = n/m.

Find the minimum number of moves to satisfy the above requirement.

Input

The first line of input contains two integers n and m (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ m ≤ n). It is guaranteed that m is a divisor of n.

The second line of input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9), the elements of the array.

Output

In the first line, print a single integer — the minimum number of moves required to satisfy the following condition: for each remainder from 0 to m - 1, the number of elements of the array having this remainder equals n/m.

In the second line, print any array satisfying the condition and can be obtained from the given array with the minimum number of moves. The values of the elements of the resulting array must not exceed 10^{18}.

Examples

Input

6 3
3 2 0 6 10 12


Output

3
3 2 0 7 10 14 


Input

4 2
0 1 2 3


Output

0
0 1 2 3 
//   package codeforces;

/**
 * Created by sky on 22/7/18.
 * www.github.com/aakashjaiswal1
 * aakashjaiswal@hotmail.co.in
 * aakashjaiswal.in@gmail.com
 * people die if they are killed
 */
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class defassult_t {
    public static void main(String[] args) {
        in = new FastReader();
        int n=ni();
        int m=ni();
        int[] arr=takeIntegerArrayInput(n);
        Queue<Integer>[] q_arr=new Queue[m];
        for (int i=0;i<m;i++){
            q_arr[i]=new LinkedList<>();
        }
        Queue<Integer> q=new LinkedList<>();
        for (int i=0;i<n;i++){
            q_arr[arr[i]%m].add(i);
        }
        int prescribed_size=n/m;
        for (int i=0;i<2*m;i++){
            int assigned_pos=i%m;
            while (q_arr[assigned_pos].size()>prescribed_size){
                int index=q_arr[assigned_pos].poll();
                ((LinkedList<Integer>) q).add(index);
            }
            while (q_arr[assigned_pos].size()<prescribed_size&&q.size()>0){
                int ele=q.poll();
                q_arr[assigned_pos].add(ele);
            }
        }
        long[] ans_arr=new long[n];
        long ans=0;
        for (int i=0;i<m;i++){
            while (q_arr[i].size()>0){
                int index=q_arr[i].poll();
                int inde_mod=arr[index]%m;
                long contri=0;
                if (i>=inde_mod){
                    contri+=i-inde_mod;
                }else{
                    contri+=m-inde_mod+i;
                }
                ans+=contri;
                ans_arr[index]=arr[index]+contri;
            }
        }
        System.out.println(ans);
        StringBuilder sb=new StringBuilder();
        for (int i=0;i<n;i++){
            sb.append(ans_arr[i]).append(" ");
        }
        System.out.println(sb.toString());
    }
    public static long binarySearch(long low, long high) {
        while (high - low > 1) {
            long mid = (high - low)/2 + low;
            //System.out.println(mid);
            if (works(mid)) {
                high = mid;
            } else {
                low = mid;
            }
        }
        return (works(low) ? low : high);
    }
    static long fast_exp_with_mod(long base, long exp) {
        long MOD=1000000000+7;
        long res=1;
        while(exp>0) {
            if(exp%2==1) res=(res*base)%MOD;
            base=(base*base)%MOD;
            exp/=2;
        }
        return res%MOD;
    }
    public static long gcd(long a, long b)
    {
        if (a == 0)
            return b;
        return gcd(b%a, a);
    }
    static class my_no{
        long num;
        long denom;

        @Override
        public String toString() {
            if (denom<0){
                this.num=-this.num;
                this.denom=-this.denom;
            }
            if (num==0)return "0";
            return (num+"/"+denom);
        }

        my_no(int no){
            this.num=no;
            this.denom=1;
        }
        my_no(long num,long denom){
            this.num=num;
            this.denom=denom;
        }

        my_no multiply(my_no obj){
            long num1=obj.num;
            long denom1=obj.denom;
            long n=num1*num;
            long d=denom1*denom;
            long gcd=gcd(n,d);
            n/=gcd;
            d/=gcd;
            return new my_no(n,d);

        }
//        my_no multiply(my_no obj){
//            long num1=obj.num;
//            long denom1=obj.denom;
//            long num2=this.num;
//            long denom2=this.denom;
//
//        }

        my_no multiply(int no){
            long n=num*no;
            long d=denom;
            long gcd=gcd(n,d);
            n/=gcd;
            d/=gcd;
            return new my_no(n,d);

        }
    }
    static void memset(int[][] arr,int val){
        for (int i=0;i<arr.length;i++){
            for (int j=0;j<arr[i].length;j++){
                arr[i][j]=val;
            }
        }
    }
    static void memset(int[] arr,int val){
        for (int i=0;i<arr.length;i++){
            arr[i]=val;
        }
    }


    static void memset(long[][] arr,long val){
        for (int i=0;i<arr.length;i++){
            for (int j=0;j<arr[i].length;j++){
                arr[i][j]=val;
            }
        }
    }
    static void memset(long[] arr,long val){
        for (int i=0;i<arr.length;i++){
            arr[i]=val;
        }
    }
    static private boolean works(long test){
        return true;
    }


    static void reverse(char[] arr ,int i,int j){
        if (i==j)
            return;
        while (i<j){
            char temp=arr[i];
            arr[i]=arr[j];
            arr[j]=temp;
            ++i;
            --j;
        }
    }
    static int[]  takeIntegerArrayInput(int no){
        int[] arr=new int[no];
        for (int i=0;i<no;++i){
            arr[i]=ni();
        }
        return arr;
    }
    static long fast_Multiply(long no , long pow){
        long result=1;
        while (pow>0){
            if ((pow&1)==1){
                result=result*no;
            }
            no=no*no;
            pow>>=1;
        }
        return result;
    }

    static long[]  takeLongArrayInput(int no){
        long[] arr=new long[no];
        for (int i=0;i<no;++i){
            arr[i]=ni();
        }
        return arr;
    }
    static final long MOD = (long)1e9+7;
    static FastReader in;


    static void p(Object o){
        System.out.print(o);
    }

    static void pn(Object o){
        System.out.println(o);
    }

    static String n(){
        return in.next();
    }

    static String nln(){
        return in.nextLine();
    }

    static int ni(){
        return Integer.parseInt(in.next());
    }

    static int[] ia(int N){
        int[] a = new int[N];
        for(int i = 0; i<N; i++)a[i] = ni();
        return a;
    }

    static long[] la(int N){
        long[] a = new long[N];
        for(int i = 0; i<N; i++)a[i] = nl();
        return a;
    }

    static long nl(){
        return Long.parseLong(in.next());
    }

    static double nd(){
        return Double.parseDouble(in.next());
    }

    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next(){
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine(){
            String str = "";
            try{
                str = br.readLine();
            }catch (IOException e){
                e.printStackTrace();
            }
            return str;
        }
    }
    static void println(String[] arr){
        for (int i=0;i<arr.length;++i){
            System.out.println(arr[i]);
        }
    }

}

