Problem: Eugeny has n cards, each of them has exactly one integer written on it. Eugeny wants to exchange some cards with Nikolay so that the number of even integers on his cards would equal the number of odd integers, and that all these numbers would be distinct. 

Nikolay has m cards, distinct numbers from 1 to m are written on them, one per card. It means that Nikolay has exactly one card with number 1, exactly one card with number 2 and so on. 

A single exchange is a process in which Eugeny gives one card to Nikolay and takes another one from those Nikolay has. Your task is to find the minimum number of card exchanges and determine which cards Eugeny should exchange.

Input

The first line contains two integers n and m (2 ≤ n ≤ 2·105, 1 ≤ m ≤ 109) — the number of cards Eugeny has and the number of cards Nikolay has. It is guaranteed that n is even.

The second line contains a sequence of n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the numbers on Eugeny's cards.

Output

If there is no answer, print -1.

Otherwise, in the first line print the minimum number of exchanges. In the second line print n integers — Eugeny's cards after all the exchanges with Nikolay. The order of cards should coincide with the card's order in the input data. If the i-th card wasn't exchanged then the i-th number should coincide with the number from the input data. Otherwise, it is considered that this card was exchanged, and the i-th number should be equal to the number on the card it was exchanged to.

If there are multiple answers, it is allowed to print any of them.

Examples

Input

6 2
5 6 7 9 4 5


Output

1
5 6 7 9 4 2 


Input

8 6
7 7 7 7 8 8 8 8


Output

6
7 2 4 6 8 1 3 5 


Input

4 1
4 2 1 10


Output

-1

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.TreeMap;
import java.util.TreeSet;

public class Q1 {
	static long MOD = 1000000007;
	static boolean b[];
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		FasterScanner sc = new FasterScanner();
		BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
		int n = sc.nextInt() , m =sc.nextInt();
		int arr[] = sc.nextIntArray(n);
		int odd = 1, even = 2;
		HashSet<Integer> hs1 = new HashSet<>();
		HashSet<Integer> hs2 = new HashSet<>();
		int g = 0, h= 0;
		for(int i = 0; i<n;i++){
			if(arr[i]%2==0){
				if(g<n/2)
				hs1.add(arr[i]);
				g++;
			}
			else if(h<n/2){
				hs2.add(arr[i]);
				h++;
			}
		}
		long ans = 0, x = hs1.size(), y = hs2.size();
		long cnt1 = (n/2)-x, cnt2 = ((n/2)-y);
		TreeSet<Integer> hs = new TreeSet<>();
		//System.out.println(cnt1+" "+cnt2);
		while(cnt1>0 && even<=m){
			if(hs1.contains(even)) even+=2;
			else{
				hs.add(even);
				cnt1--;
				even+=2;
			}
		}
		while(cnt2>0 && odd<=m){
			if(hs2.contains(odd)) odd+=2;
			else{
				hs.add(odd);
				cnt2--;
				odd+=2;
			}
		}
	//	System.out.println(hs);
		if(cnt1 == 0&&cnt2==0){
		System.out.println(n-x-y);
		for(int i = 0;i<n;i++){
			if(hs1.contains(arr[i])){
				hs1.remove(arr[i]);
			}
			else if(hs2.contains(arr[i])) hs2.remove(arr[i]);
			else{
				arr[i] = hs.pollFirst();
			}
			System.out.print(arr[i]+" ");
		}
		}
		else System.out.println("-1");
		log.close();
	}
	public static void seive(long n){
		b = new boolean[(int) (n+1)];
		Arrays.fill(b, true);
		for(int i = 2;i<=n;i++){
			if(b[i]){
				for(int p = 2*i;p<=n;p++){
					b[p] = false;
				}
			}
		}
	}
	static long modInverse(long a, long mOD2){
	            return  power(a, mOD2-2, mOD2);
	}
	static long power(long x, long y, long m)
	{
	    if (y == 0)
	        return 1;
	    long p = power(x, y/2, m) % m;
	    p = (p * p) % m;
	 
	    return (y%2 == 0)? p : (x * p) % m;
	}
	static long d,x,y;
	public static void extendedEuclidian(long a, long b){
		if(b == 0) {
	        d = a;
	        x = 1;
	        y = 0;
	    }
	    else {
	        extendedEuclidian(b, a%b);
	        int temp = (int) x;
	        x = y;
	        y = temp - (a/b)*y;
	    }
	}
	public static long inverseModulo(long n){
		return powerModulo(n, MOD-2);
	}
	public static long gcd(long n, long m){
		if(m!=0) return gcd(m,n%m);
		else return n;
	}
	public static long powerModulo(long x, long y){
		long ans = 1;
		while(y>0){
			if(y%2==1){
				ans = (ans%MOD*x%MOD)%MOD;
				y--;
			}
			else{
				x = (x%MOD*x%MOD)%MOD;
				y/=2;
			}
		}
	return ans;
	}
	static class Pair implements Comparable<Pair> {
		int u;
		int v;
		public Pair(){
			
		}
		public Pair(int u, int v) {
			this.u = u;
			this.v = v;
		}
		
		public int hashCode() {
			int hu = (int) (u ^ (u >>> 32));
			int hv = (int) (v ^ (v >>> 32));
			return 31*hu + hv;
		}

		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return (u == other.u && v == other.v);
		}

		public int compareTo(Pair other) {
			return Integer.compare(u, other.u) != 0 ? (Integer.compare(u, other.u)) : (Integer.compare(v, other.v));
		}

		public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}
	}
	public static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
 
		public int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 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) {
	        return nextIntArray(n, 0);
	    }
	    
	    public int[] nextIntArray(int n, int off) {
	    	int[] arr = new int[n + off];
	    	for (int i = 0; i < n; i++) {
	    		arr[i + off] = nextInt();
	    	}
	    	return arr;
	    }
	    
	    public long[] nextLongArray(int n) {
	    	return nextLongArray(n, 0);
	    }
        
		public long[] nextLongArray(int n, int off) {
		    long[] arr = new long[n + off];
		    for (int i = 0; i < n; i++) {
		        arr[i + off] = 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;
		}
	}
}