There is an array with n elements a1, a2, ..., an and the number x.

In one operation you can select some i (1 ≤ i ≤ n) and replace element ai with ai & x, where & denotes the [bitwise and](https://en.wikipedia.org/wiki/Bitwise_operation#AND) operation.

You want the array to have at least two equal elements after applying some operations (possibly, none). In other words, there should be at least two distinct indices i ≠ j such that ai = aj. Determine whether it is possible to achieve and, if possible, the minimal number of operations to apply.

Input

The first line contains integers n and x (2 ≤ n ≤ 100 000, 1 ≤ x ≤ 100 000), number of elements in the array and the number to and with.

The second line contains n integers ai (1 ≤ ai ≤ 100 000), the elements of the array.

Output

Print a single integer denoting the minimal number of operations to do, or -1, if it is impossible.

Examples

Input

4 3
1 2 3 7


Output

1


Input

2 228
1 1


Output

0


Input

3 7
1 2 3


Output

-1

Note

In the first example one can apply the operation to the last element of the array. That replaces 7 with 3, so we achieve the goal in one move.

In the second example the array already has two equal elements.

In the third example applying the operation won't change the array at all, so it is impossible to make some pair of elements equal.

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

public class Main
{
 
	private static final Comparator<? super Integer> Comparator = null;
	static LinkedList<Integer> adj[];
	static ArrayList<Integer> adj1[];
	static int[] color,visited1;
	static boolean b[],visited[],possible;
	static int level[];
	static Map<Integer,HashSet<Integer>> s;
	static int totalnodes,colored;
	static int count[];
	static long sum[];
	static int nodes;
	static long ans=0;
	static long[] as=new long[10001];
	static long c1=0,c2=0;
	static int[] a,d,k;
	static int max=100000000;
	static long MOD = 1000000007,sm=0,m=Long.MIN_VALUE;
	static boolean[] prime=new boolean[1000005];
	static int[] levl;
    static int[] eat;
    static int price[];
    static int res[],par[],co[];
    static int result=0;
    static int[] root,size,du,dv;
    static long p=Long.MAX_VALUE;
    static int start,end,r=0;
    static boolean[] vis1,vis2;
    static int to;
    static HashMap<Pair,Integer> hs;
    static boolean ns;
   
    static String st,t;
    static long n;
  
	// --------------------My Code Starts Here----------------------
	
	public static void main(String[] args) throws IOException
	{
		in=new InputReader(System.in);
	    w=new PrintWriter(System.out);
	    
	
	    int n=ni();
	      long x=nl();
	      int min=Integer.MAX_VALUE;
	      long[] a=new long[n];
	      long[] b=new long[n];
	      HashSet<Long> h1=new HashSet<Long>();
	      HashSet<Long> h2=new HashSet<Long>();
	      for(int i=0;i<n;i++)
	      {
	    	  a[i]=nl();
	    	 
	    	  b[i]=a[i]&x;
	    	  //w.println(b[i]);
	    
	    	  if((h1.contains(b[i]) || h2.contains(a[i])))
	    			  {
	    		          min=Math.min(min,1);
	    			  }
	    	  if(h1.contains(a[i]))
	    		  min=Math.min(min,0);
	    	  if(h2.contains(b[i]))
	    		  min=Math.min(min,2);
	    	  h1.add(a[i]);
	    	  h2.add(b[i]);
	 
	    
	      }
	      
	      if(min==Integer.MAX_VALUE)
	    	  w.print(-1);
	      else
	    	  w.print(min);
  
	    
	    
    w.close();
	}

	
	
	
	// --------------------My Code Ends Here------------------------

	static class Pair implements Comparable<Pair>
	 {
		Integer a;

		
	     
	        Pair(int a)
	        {
	            this.a=a;
//	            this.b=b;
	            //this.l=l;
	     
	        }
	        public int compareTo(Pair p)
	        {
	  //      	if(this.a==p.a)
	//        	   return Long.compare(this.b,p.b);
	    //    	else
	        		return Long.compare(this.a,p.a);
	        }
		
	}

	public static void swap(int[] a,int l,int r)
	{
		int t=a[l];
		a[l]=a[r];
		a[r]=t;
	}
	public static void swap(long[] a,int l,int r)
	{
		long t=a[l];
		a[l]=a[r];
		a[r]=t;
	}
	public static void sort(long[] a)
	{
	   ArrayList<Long> al=new ArrayList<Long>();
	   for(int i=0;i<a.length;i++)
		   al.add(a[i]);
	   Collections.sort(al);
	   for(int i=0;i<a.length;i++)
		   a[i]=al.get(i);
	}
	public static long pow(long a, long b, long c) {
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}



     

	
	
	/*
	 *  PriorityQueue<Integer> pq = new PriorityQueue<Integer>(new Comparator<Integer>()
  			{
  				public int compare(Integer o1, Integer o2)
  				{
  					return Intege
  					r.compare(o2,o1);
  				}
  			});
	 * 
	 * 
	 */
	
	public static void shuffle(long[] a,int n)
	{
		Random r=new Random();
		for(int i=n-1;i>0;i--)
		{
			int j=r.nextInt(i);
			swap(a,j,i);
		}
	}



	 public static void buildgraph(int n)
	 {
         adj=new LinkedList[n+1];
         visited=new boolean[n];
         level=new int[n];
         par=new int[n];
         for(int i=0;i<=n;i++)
         	{
        	 adj[i]=new LinkedList<Integer>();
         	
         	}
      
	 }
	
	/*public static long kruskal(Pair[] p)
	{
		long ans=0;
		int w=0,x=0,y=0;
		for(int i=0;i<p.length;i++)
		{
			w=p[i].w;
			x=p[i].x;
			y=p[i].y;
			if(root(x)!=root(y))
			{
				ans+=w;
				union(x,y);
			}
		}
		return ans;
	}*/

	public static int root(int i)
	{
		while(root[i]!=i)
		{
			root[i]=root[root[i]];
			i=root[i];
		}
		return i;
	}
	
	public static void init(int n)
	{
		root=new int[n+1];
		for(int i=1;i<=n;i++)
			root[i]=i;
	}
	public static void union(int a,int b)
	{
	    int root_a=root(a);	
	    int root_b=root(b);
	    root[root_a]=root_b;
	   // size[root_b]+=size[root_a];
	}


	
	public static boolean isPrime(long n)
	{
	    if (n <= 1)  return false;
	    if (n <= 3)  return true;
	    
	    if (n%2 == 0 || n%3 == 0)
	    	return false;
	 
	    for (long i=5; i*i<=n; i=i+6)
	        if (n%i == 0 || n%(i+2) == 0)
	           return false;
	 
	    return true;
	}
	

	
	public static String ns()
	{
		return in.nextLine();
	}
	public static int ni()
	{
		return in.nextInt();
	}
	public static long nl()
	{
		return in.nextLong();
	}
	public static int[] na(int n)
	{
		int[] a=new int[n];
		for(int i=0;i<n;i++)
		a[i]=ni();
		return a;
	}
	public static long[] nla(int n)
	{
		long[] a=new long[n];
		for(int i=0;i<n;i++)
		a[i]=nl();
		return a;
	}
	public static void sieve()
	    {
	       int n=prime.length;
	        for(int i=0;i<n;i++)
	            prime[i] = true;
	         
	        for(int p = 2; p*p <=n; p++)
	        {
	            if(prime[p])
	            {
	                for(int i = p*2; i <n; i += p)
	                    prime[i] = false;
	            }
	        }
	    }

  public static String rev(String s)
	{
		StringBuilder sb=new StringBuilder(s);
	
	    sb.reverse();
		return sb.toString();
	}
/*	static long lcm(long a, long b)
	{
	    return a * (b / gcd(a, b));
	}*/
	static int gcd(int a, int b)
	{
	    while (b > 0)
	    {
	        int temp = b;
	        b = a % b; // % is remainder
	        a = temp;
	    }
	    return a;
	}
	static InputReader in;
	static PrintWriter w;
static class InputReader 
{
 
private final InputStream stream;
private final byte[] buf = new byte[8192];
private int curChar, snumChars;
private SpaceCharFilter filter;
 
public InputReader(InputStream stream)
{
  this.stream = stream;
}
 
public int snext()
{
  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 = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  int res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}
 
public long nextLong() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  int sgn = 1;
  if (c == '-')
  {
    sgn = -1;
    c = snext();
  }
  long res = 0;
  do
  {
    if (c < '0' || c > '9')
      throw new InputMismatchException();
    res *= 10;
    res += c - '0';
    c = snext();
  }
  while (!isSpaceChar(c));
  return res * sgn;
}	    
public String readString() 
{
  int c = snext();
  while (isSpaceChar(c)) 
  {
    c = snext();
  }
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isSpaceChar(c));
  return res.toString();
}
 
public String nextLine() 
{
  int c = snext();
  while (isSpaceChar(c))
    c = snext();
  StringBuilder res = new StringBuilder();
  do
  {
    res.appendCodePoint(c);
    c = snext();
  }
  while (!isEndOfLine(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;
}
 
private boolean isEndOfLine(int c) 
{
  return c == '\n' || c == '\r' || c == -1;
}
 
public interface SpaceCharFilter
{
  public boolean isSpaceChar(int ch);
}
}
	
}