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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;
		public class Main implements Runnable
		{
			static final long MOD = 1000000007L;
			static final long MOD2 = 1000000009L;
			static class InputReader
			{
				private InputStream stream;
				private byte[] buf = new byte[1024];
				private int curChar;
				private int numChars;
				private SpaceCharFilter filter;
				private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		 
				public InputReader(InputStream stream)
				{
					this.stream = stream;
				}
				
				public int read()
				{
					if (numChars==-1) 
						throw new InputMismatchException();
					
					if (curChar >= numChars)
					{
						curChar = 0;
						try 
						{
							numChars = stream.read(buf);
						}
						catch (IOException e)
						{
							throw new InputMismatchException();
						}
						
						if(numChars <= 0)				
							return -1;
					}
					return buf[curChar++];
				}
			 
				public String nextLine()
				{
					String str = "";
		            try
		            {
		                str = br.readLine();
		            }
		            catch (IOException e)
		            {
		                e.printStackTrace();
		            }
		            return str;
				}
				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 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 double nextDouble() 
				{
					int c = read();
					while (isSpaceChar(c))
						c = read();
					int sgn = 1;
					if (c == '-') 
					{
						sgn = -1;
						c = read();
					}
					double res = 0;
					while (!isSpaceChar(c) && c != '.') 
					{
						if (c == 'e' || c == 'E')
							return res * Math.pow(10, nextInt());
						if (c < '0' || c > '9')
							throw new InputMismatchException();
						res *= 10;
						res += c - '0';
						c = read();
					}
					if (c == '.') 
					{
						c = read();
						double m = 1;
						while (!isSpaceChar(c)) 
						{
							if (c == 'e' || c == 'E')
								return res * Math.pow(10, nextInt());
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							m /= 10;
							res += (c - '0') * m;
							c = read();
						}
					}
					return res * sgn;
				}
				
				public String readString() 
				{
					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 boolean isSpaceChar(int c) 
				{
					if (filter != null)
						return filter.isSpaceChar(c);
					return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
				}
			 
				public String next() 
				{
					return readString();
				}
				
				public interface SpaceCharFilter 
				{
					public boolean isSpaceChar(int ch);
				}
			}
		 	
			public static void main(String args[]) throws Exception
			{
				new Thread(null, new Main(),"Main",1<<26).start();
			}
			int MAXN = 1000001;
			public void run() 
			{
				InputReader sc= new InputReader(System.in);
				PrintWriter w= new PrintWriter(System.out);
				int n = sc.nextInt();
				int m = sc.nextInt();
				int[] arr = new int[n];
				int[] cnt=  new int[m];
				for(int i = 0;i < n;i++) {
					arr[i] = sc.nextInt();
					cnt[arr[i] % m]++;
				}
				TreeMap<Integer,Integer> tmap = new TreeMap();
				for(int i = 0;i < m;i++) {
					if(cnt[i] < n/m) {
						tmap.put(i,n/m - cnt[i]);
					}
				}
				int[] ans = new int[n];
				long fans = 0;
				for(int i = 0;i < n;i++) {
					if(cnt[arr[i] % m] > n/m){
						Integer key = tmap.higherKey(arr[i] % m);
						if(key != null) {
							cnt[key]++;
							cnt[arr[i] % m]--;
							fans += (key - (arr[i] % m));
							ans[i] = arr[i] + (key - (arr[i] % m));
							if(tmap.get(key) > 1) {
								tmap.put(key,tmap.get(key) - 1);
							}else {
								tmap.remove(key);
							}
							
						}else {
							Integer key2 = tmap.ceilingKey(0);
							cnt[key2]++;
							cnt[arr[i] % m]--;
							ans[i] = arr[i] + (m - (arr[i] % m)) + key2;
							fans += (m - (arr[i] % m) + key2);
							if(tmap.get(key2) > 1) {
								tmap.put(key2,tmap.get(key2) - 1);
							}else {
								tmap.remove(key2);
							}
						}
					}else {
						ans[i] = arr[i];
					}
				}
				w.println(fans);
				for(int i = 0;i < n;i++) {
					w.print(ans[i] + " ");
				}
				w.close();
			}
			String reverse(String a) {
				String navi = "";
				for(int i = a.length()-1;i >= 0;i--) {
					navi += a.charAt(i);
				}
				return navi;
			}
			static boolean isPrime(long n)
		    {
		        // Corner cases
		        if (n <= 1) return false;
		        if (n <= 3) return true;
		     
		        // This is checked so that we can skip 
		        // middle five numbers in below loop
		        if (n % 2 == 0 || n % 3 == 0) return false;
		     
		        for (int i = 5; i * i <= n; i = i + 6)
		            if (n % i == 0 || n % (i + 2) == 0)
		            return false;
		     
		        return true;
		    }
		 
			long count = 0;
			long[][] dist;
			void flydwarShall(int k,int size) {
				for(int i = 0;i < size;i++) {
					for(int j = 0;j < size;j++) {
						if(dist[i][j] > dist[i][k] + dist[k][j]) {
							dist[i][j] = dist[i][k] + dist[k][j];
						}
					}
				}
			}
			Pair[] segTree;
			int[] arr;
			void build(int l,int r,int pos) {
				if(l == r) {
					segTree[pos] = new Pair(1,1,1,arr[l],arr[l],true);
					return;
				}
				int mid = (l + r) >> 1;
				build(l,mid,2*pos+1);
				build(mid+1, r, 2*pos+2);
				segTree[pos] = merge(segTree[2*pos+1], segTree[2*pos+2]);
			}
			Pair merge(Pair p1,Pair p2) {
				if(p1.val1 == 0) {
					return p2;
				}else if(p2.val1 == 0) {
					return p1;
				}
				Pair navi = new Pair();
				navi.val1 = p1.val1;
				navi.val2 = p2.val2;
				if(p1.val2 == p2.val1) {
					navi.max = Math.max(p1.max,p2.max);
					navi.first = p1.first;
					navi.second = p2.second;
					navi.whole = false;
				}else {
					navi.max = Math.max(p1.max,Math.max(p2.max,p1.second + p2.first));
					if(p1.whole && p2.whole) {
						navi.first = p1.first + p2.first;
						navi.second = p1.first + p2.first;
						navi.whole = true;
					}else if(p1.whole) {
						navi.first = p1.first + p2.first;
						navi.second = p2.second;
						navi.whole = false;
					}else if(p2.whole) {
						navi.first = p1.first;
						navi.second = p1.second + p2.first;
						navi.whole = false;
					}else {
						navi.first = p1.first;
						navi.second = p2.second;
						navi.whole = false;
					}
				}
				return navi;
			}
			Pair query(int pos, int l, int r, int start, int end)
			{
			    if(end < l || r < start)
			    {
			        return new Pair(0,0,0,0,0,false);
			    }
			    if(start <= l && r <= end)
			    {
			        // range represented by a node is completely inside the given range
			        return segTree[pos];
			    }
			    // range represented by a node is partially inside and partially outside the given range
			    int mid = (l + r) / 2;
			    Pair p1 = query(2*pos + 1, l, mid, start, end);
			    Pair p2 = query(2*pos+2, mid+1, r, start, end);
			    return merge(p1, p2);
			}
			int bsearch(Integer[] arr,int l,int r,int val) {
				int ind = -1;
				while(l <= r) {
					int mid = (l + r)/2;
					if(arr[mid] <= val) {
						l = mid + 1;
						ind = mid;
					}else {
						r = mid - 1;
					}
				}
				return ind;
			}
			Stack<Integer> st = new Stack();
			int bridges = 0;
			
			
			long modExpo(long a,long pow,long mod) {
				long res = 1;
				while(pow > 0) {
					if(pow % 2 == 1) {
						res = (res * a) % mod;
					}
					pow = pow/2;
					a = (a * a) % mod;
				}
				return res;
			}
			  static long modInverse(long a, long m)
			    {
			        
			       
			            // If a and m are relatively prime, then modulo inverse
			            // is a^(m-2) mode m
			         
			                        return        power(a, m - 2, m);
			        
			    }
			     
			    // To compute x^y under modulo m
			// Iterative Java program to 
			// compute modular power
			
			    static long power(long x, long y,long p)
			    {
			        // Initialize result
			        long res = 1;     
			        
			        // Update x if it is more  
			        // than or equal to p
			        x = x % p; 
			     
			        while (y > 0)
			        {
			            // If y is odd, multiply x
			            // with result
			            if((y & 1)==1)
			                res = (res * x) % p;
			     
			            // y must be even now
			            // y = y / 2
			            y = y >> 1; 
			            x = (x * x) % p; 
			        }
			        return res;
			    }
			static class Temp implements Comparable<Temp>{
				int a;
				int b;
				Temp(int a,int b){
					this.a = a;
					this.b = b;
				}
				@Override
				public int compareTo(Temp t){
					return Double.compare(this.a,t.a);
				}
			}
			static class Pair implements Comparable<Pair>{
				int first;
				int max;
				int second;
				int val1;
				int val2;
				boolean whole;
				
				Pair (int a,int b,int c,int val1,int val2,boolean whole){
					this.first = a;
					this.max = b;
					this.second = c;
					this.val1= val1;
					this.val2 = val2;
					this.whole = whole;
				}
				Pair(){
					
				}
				public boolean equals(Object o)
				{
					Pair p = (Pair)o;
					return (p.first==first && p.max==max) || (p.first == max && p.first == max);
				}
				public int hashCode()
				{
					return new Long(first).hashCode()*31 + new Long(max).hashCode();
				}
				public int compareTo(Pair p){
					return Long.compare(p.first,this.first);
				}
			}
		
		}