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.*;
import java.util.*;
 
 
 
public class Main {
	
	static InputReader in = new InputReader(System.in);
	static PrintWriter out = new PrintWriter(System.out);
	
	static int oo = (int)1e9;
	static int mod = 1000000007;
	
	public static void main(String[] args) throws IOException {

		int n = in.nextInt();
		int m = in.nextInt();
		int[] a = new int[n];
		HashMap<Integer, Integer> map = new HashMap<>();
		int odd = 0, even = 0;
		for(int i = 0; i < n; ++i) {
			a[i] = in.nextInt();
			map.put(a[i], map.getOrDefault(a[i], 0) + 1);
			if(a[i] % 2 == 0)
				even++;
			else
				odd++;
		}
		int o = 1, e = 2;
		int cnt = 0;
		for(int i = 0; i < n; ++i) {
			if(map.get(a[i]) > 1) {
				if(odd > even || odd == even && a[i] % 2 == 0) {
					while(e <= m) {
						if(!map.containsKey(e)) {
							if(a[i] % 2 == 1) {
								even++;
								odd--;
							}
							change(a, map, i, e);	
							cnt++;
							break;
						}
						e += 2;
					}
				}
				else if(even > odd || odd == even && a[i] % 2 == 1) {
					while(o <= m) {
						if(!map.containsKey(o)) {
							if(a[i] % 2 == 0) {
								odd++;
								even--;
							}
							change(a, map, i, o);
							cnt++;
							break;
						}
						o += 2;
					}
				}
			}
		}
		
		for(int i = 0; i < n; ++i) {
			if(odd > even && a[i] % 2 == 1) {
				while(e <= m) {
					if(!map.containsKey(e)) {
						change(a, map, i, e);
						cnt++;
						even++;
						odd--;
						break;
					}
					e += 2;
				}
			}
			else if(odd < even && a[i] % 2 == 0) {
				while(o <= m) {
					if(!map.containsKey(o)) {
						change(a, map, i, o);
						cnt++;
						even--;
						odd++;
						break;
					}
					o += 2;
				}
			}
		}
		for(int i = 0; i < n; ++i) {
			if(map.get(a[i]) > 1) {
				out.println(-1);
				out.close();
				return;
			}
		}
		if(odd != even)
			out.println(-1);
		else {
			out.println(cnt);
			for(int x : a)
				out.print(x + " ");
		}
		
		out.close();
	}
	
	static void change(int[] a, HashMap<Integer, Integer> map, int i, int value) {
		int cnt = map.get(a[i]);
		if(--cnt == 0) 
			map.remove(a[i]);
		else
			map.put(a[i], cnt);
		a[i] = value;
		map.put(a[i], map.getOrDefault(a[i], 0) + 1);
	}
	
	static long solve(ArrayList<Integer>[] adj, boolean[] visit, long[] best, int u) {
		if(visit[u])
			return 0;
		visit[u] = true;
		PriorityQueue<Long> pq = new PriorityQueue<>(Collections.reverseOrder());
		long ret = Long.MIN_VALUE;
		for(int v : adj[u]) {
			if(!visit[v]) {
				pq.add(best[v]);
				ret = Math.max(ret, solve(adj, visit, best, v));
			}
		}
		if(pq.size() >= 2) {
			ret = Math.max(ret, pq.poll() + pq.poll() );
		}
		return ret;
	}
	
	
	static long getSum(ArrayList<Integer>[] adj, boolean[] visit, int[] a, long[] sum, int u) {
		if(visit[u])
			return 0;
		visit[u] = true;
		long ret = a[u];
		for(int v : adj[u]) {
			if(!visit[v])
				ret += getSum(adj, visit, a, sum, v);
		}
		return sum[u] = ret;
	}
	
	static long getBest(ArrayList<Integer>[] adj, boolean[] visit, long[] sum, long[] best, int u) {
		if(visit[u])
			return 0;
		visit[u] = true;
		long ret = Long.MIN_VALUE;
		for(int v : adj[u]) {
			if(!visit[v]) {
				ret = Math.max(ret, getBest(adj, visit, sum, best, v));
			}
		}
		ret = Math.max(ret, sum[u]);
		return best[u] = ret;
	}
	
	static class SegmentTree {
		int n;
		long[] a, seg;
		int DEFAULT_VALUE = 0;
		
		public SegmentTree(long[] a, int n) {
			super();
			this.a = a;
			this.n = n;
			seg = new long[n * 4 + 1];
			build(1, 0, n-1);
		}
		
		private long build(int node, int i, int j) {
			if(i == j)
				return seg[node] = a[i];
			long first = build(node * 2, i, (i+j) / 2);
			long second = build(node * 2 + 1, (i+j) / 2 + 1, j);
			return seg[node] = combine(first, second);
		}
		
		long update(int k, long value) {
			return update(1, 0, n-1, k, value);
		}
		
		private long update(int node, int i, int j, int k, long value) {
			if(k < i || k > j)
				return seg[node];
			if(i == j && j == k) {
				a[k] = value;
				seg[node] = value;
				return value;
			}
			
			int m = (i + j) / 2;
			long first = update(node * 2, i, m, k, value);
			long second = update(node * 2 + 1, m + 1, j, k, value);
			return seg[node] = combine(first, second);
		}
		
		long query(int l, int r) {
			return query(1, 0, n-1, l, r);
		}
		
		private long query(int node, int i, int j, int l, int r) {
			if(l <= i && j <= r)
				return seg[node];
			if(j < l || i > r)
				return DEFAULT_VALUE;
			int m = (i + j) / 2;
			long first = query(node * 2, i, m, l, r);
			long second = query(node * 2 + 1, m+1, j, l, r);
			return combine(first, second);
		}

		private long combine(long a, long b) {
			return a + b;
		}
	}
	
	static class DisjointSet {
		int n;
		int[] g;
		int[] h;
		public DisjointSet(int n) {
			super();
			this.n = n;
			g = new int[n];
			h = new int[n];
			for(int i = 0; i < n; ++i) {
				g[i] = i;
				h[i] = 1;
			}
		}
		int find(int x) {
			if(g[x] == x)
				return x;
			return g[x] = find(g[x]);
		}
		void union(int x, int y) {
			x = find(x); y = find(y);
			if(x == y)
				return;
			if(h[x] >= h[y]) {
				g[y] = x;
				if(h[x] == h[y])
					h[x]++;
			}
			else {
				g[x] = y;
			}
		}
	}
	
	
	static int[] getPi(char[] a) {
		int m = a.length;
		int j = 0;
		int[] pi = new int[m];
		for(int i = 1; i < m; ++i) {
			while(j > 0 && a[i] != a[j])
				j = pi[j-1];
			if(a[i] == a[j]) {
				pi[i] = j + 1;
				j++;
			}
		}
		return pi;
	}
	
	static long lcm(long a, long b) {
		return a * b / gcd(a, b);
	}
	
	static boolean nextPermutation(int[] a) {
		for(int i = a.length - 2; i >= 0; --i) {
			if(a[i] < a[i+1]) {
				for(int j = a.length - 1; ; --j) {
					if(a[i] < a[j]) {
						int t = a[i];
						a[i] = a[j];
						a[j] = t;
						for(i++, j = a.length - 1; i < j; ++i, --j) {
							t = a[i];
							a[i] = a[j];
							a[j] = t;
						}
						return true;
					}
				}
			}
		}
		return false;
	}
	
	
	static void shuffle(int[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			int t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static void shuffle(long[] a) {
		Random r = new Random();
		for(int i = a.length - 1; i > 0; --i) {
			int si = r.nextInt(i);
			long t = a[si];
			a[si] = a[i];
			a[i] = t;
		}
	}
	
	static int lower_bound(int[] a, int n, int k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	static int lower_bound(long[] a, int n, long k) {
		int s = 0;
		int e = n;
		int m;
		while (e - s > 0) {
			m = (s + e) / 2;
			if (a[m] < k)
				s = m + 1;
			else
				e = m;
		}
		return e;
	}
	
	static int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	static long gcd(long a, long b) {
		return b == 0 ? a : gcd(b, a % b);
	}
	
	static class Pair implements Comparable<Pair> {
		int first, second;
 
		public Pair(int first, int second) {
			super();
			this.first = first;
			this.second = second;
		}
 
		@Override
		public int compareTo(Pair o) {
			return this.first != o.first ? this.first - o.first : this.second - o.second;
		}
 
		@Override
		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + first;
			result = prime * result + second;
			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 (first != other.first)
				return false;
			if (second != other.second)
				return false;
			return true;
		}
	}
}
 
 
 
class InputReader {
 
	private final InputStream stream;
	private final byte[] buf = new byte[8192];
	private int curChar, snumChars;
 
	public InputReader(InputStream st) {
		this.stream = st;
	}
 
	public int read() {
		if (snumChars == -1)
			throw new InputMismatchException();
		if (curChar >= snumChars) {
			curChar = 0;
			try {
				snumChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (snumChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}
 
	public int nextInt() {
		int c = read();
		while (isSpaceChar(c)) {
			c = read();
		}
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			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 {
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
 
	public int[] nextIntArray(int n) {
		int a[] = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		return a;
	}
 
	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 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 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;
	}
 
}