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 

import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.fill;
import static java.lang.Math.*;
import static java.util.Arrays.sort;
import static java.util.Collections.sort;


public class D978 
{

	public static int mod = 1000000007;
	public static long INF = (1L << 60);
	static FastScanner2 in = new FastScanner2();
	static OutputWriter out = new OutputWriter(System.out);
 
	
	
	static class Pair implements Comparable<Pair>
	{
		int rem,freq;
		Pair(int rem,int freq)
		{
			this.rem=rem;
			this.freq=freq;
		}
		public int compareTo(Pair p)
		{
			if(this.rem==p.rem)
			{
				return this.freq-p.freq;
			}
			return this.rem-p.rem;
		}
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + freq;
			result = prime * result + rem;
			return result;
		}
		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (freq != other.freq)
				return false;
			if (rem != other.rem)
				return false;
			return true;
		}
	}
	
	public static void main(String[] args) 
	{


		int n=in.nextInt();
		int m=in.nextInt();
		long[] a=new long[n];
		for(int i=0;i<n;i++)
		{
			a[i]=in.nextLong();
		}
		int tomake=n/m;
		int[] count=new int[m];
		TreeSet<Pair> ts=new TreeSet<>();
		for(int i=0;i<n;i++)
		{
			int rem=(int) (a[i]%m);
			count[rem]++;
		}
		for(int i=0;i<m;i++)
		{
			if(count[i]<tomake)
			{
				ts.add(new Pair(i, 0));
			}
		}
		int[] curcame=new int[m];
		long ans=0;
		for(int i=0;i<n;i++)
		{
			int rem=(int)(a[i]%m);
			if(ts.contains(new Pair(rem, curcame[rem])))
				ts.remove(new Pair(rem, curcame[rem]));
			curcame[rem]++;
			if(curcame[rem]<tomake)
				ts.add(new Pair(rem, curcame[rem]));
			if(curcame[rem]>tomake)
			{

				Pair p=(ts.higher(new Pair(rem, 1))!=null)?ts.higher(new Pair(rem, 1)):ts.first();
				long goalrem=p.rem;
				if(goalrem>rem)
				{
					ans+=(goalrem-rem);
					a[i]+=(goalrem-rem);
				}
				else
				{
					ans+=(m-rem+goalrem);
					a[i]+=(m-rem+goalrem);
				}
				curcame[(int) goalrem]++;
				ts.remove(p);
				if(curcame[(int)goalrem]<tomake)
				ts.add(new Pair((int)goalrem, curcame[(int)goalrem]));
				curcame[rem]--;
			}
		}
		out.println(ans);
		for(int i=0;i<n;i++)
		{
			out.print(a[i]+" ");
		}
		out.close();

	}
	

	static class FastScanner2 
	{
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() 
		{
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) 
			{
				curChar = 0;
				try 
				{
					snumChars = System.in.read(buf);
				} catch (IOException e) 
				{
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong()
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} 
			while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} 
			while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n)
		{
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) 
			{
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n)
		{
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) 
			{
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c)
		{
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) 
		{
			return c == '\n' || c == '\r' || c == -1;
		}
	}


	static class OutputWriter 
	{
		private final PrintWriter writer;

		public OutputWriter(OutputStream outputStream) 
		{
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}

		public OutputWriter(Writer writer)
		{
			this.writer = new PrintWriter(writer);
		}

		public void print(Object... objects)
		{
			for (int i = 0; i < objects.length; i++) 
			{
				if (i != 0)
					writer.print(' ');
				writer.print(objects[i]);
			}
		}

		public void println(Object... objects)
		{
			print(objects);
			writer.println();
		}

		public void close() 
		{
			writer.close();
		}

		public void flush() 
		{
			writer.flush();
		}
	}
private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	
	private static void debug(Object... o) 
	{
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
	private static void tr(Object... o) 
	{
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}