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

public class Stack3 {

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }
            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    static Reader sc = new Reader();
    static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
    static long mod = (long) (1e9 + 7);

    public static void main(String[] args) throws IOException {
        /*
         * For integer input: int n=inputInt();
         * For long input: long n=inputLong();
         * For double input: double n=inputDouble();
         * For String input: String s=inputString();
         * Logic goes here
         * For printing without space: print(a+""); where a is a variable of any datatype
         * For printing with space: printSp(a+""); where a is a variable of any datatype
         * For printing with new line: println(a+""); where a is a variable of any datatype
         */
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int x = sc.nextInt();
        //int[] ar=new int[n];
        List<Integer> list = new ArrayList<>();
        Set<Integer> set = new HashSet<>();
        boolean[] check=new boolean[100000+1];
        for (int i = 0; i < n; i++) {
            int num = sc.nextInt();
           check[num]=true;
            list.add(num);
            set.add(num);
        }
        if (set.size() < n) {
            System.out.println(0);
        } else {
            Set<Integer> f1=new HashSet<>();
            for (int j = 0; j < list.size(); j++) {
                int num = list.get(j) & x;
               /* int i1 = list.indexOf(num);
                int i2 = list.lastIndexOf(num);*/
               if(num!=list.get(j)&&num<=100000){
                   if(check[num]){
                       System.out.println(1);
                       return;
                   }
               }
                f1.add(num);


            }
            if(f1.size()<n){
                System.out.println(2);
            }else {
                System.out.println(-1);
            }

        }


        bw.flush();
        bw.close();


    }


    public static void dfs1(List<List<Integer>> g, boolean[] visited, Stack<Integer> stack, int num) {
        visited[num] = true;
        for (Integer integer : g.get(num)) {
            if (!visited[integer]) {
                dfs1(g, visited, stack, integer);
            }
        }
        stack.push(num);
    }

    public static void dfs2(List<List<Integer>> g, boolean[] visited, List<Integer> list, int num, int c, int[] raj) {
        visited[num] = true;

        for (Integer integer : g.get(num)) {
            if (!visited[integer]) {
                dfs2(g, visited, list, integer, c, raj);
            }
        }
        raj[num] = c;
        list.add(num);

    }

    public static int inputInt() throws IOException {
        return sc.nextInt();
    }

    public static long inputLong() throws IOException {
        return sc.nextLong();
    }

    public static double inputDouble() throws IOException {
        return sc.nextDouble();
    }

    public static String inputString() throws IOException {
        return sc.readLine();
    }

    public static void print(String a) throws IOException {
        bw.write(a);
    }

    public static void printSp(String a) throws IOException {
        bw.write(a + " ");
    }

    public static void println(String a) throws IOException {
        bw.write(a + "\n");
    }


    public static long getAns(int[] ar, int c, long[][] dp, int i, int sign) {
        if (i < 0) {
            return 1;
        }

        if (c <= 0) {
            return 1;
        }

        dp[i][c] = Math.max(dp[i][c], Math.max(ar[i] * getAns(ar, c - 1, dp, i - 1, sign), getAns(ar, c, dp, i - 1, 1)));
        return dp[i][c];
    }


    public static long power(long a, long b, long c) {
        long ans = 1;
        while (b != 0) {
            if (b % 2 == 1) {
                ans = ans * a;
                ans %= c;
            }
            a = a * a;
            a %= c;
            b /= 2;
        }
        return ans;
    }

    public static long power1(long a, long b, long c) {
        long ans = 1;
        while (b != 0) {
            if (b % 2 == 1) {
                ans = multiply(ans, a, c);
            }
            a = multiply(a, a, c);
            b /= 2;

        }
        return ans;

    }

    public static long multiply(long a, long b, long c) {
        long res = 0;
        a %= c;
        while (b > 0) {
            if (b % 2 == 1) {
                res = (res + a) % c;
            }
            a = (a + a) % c;
            b /= 2;
        }

        return res % c;

    }

    public static long totient(long n) {
        long result = n;
        for (long i = 2; i * i <= n; i++) {
            if (n % i == 0) {
                //sum=sum+2*i;
                while (n % i == 0) {
                    n /= i;
                    // sum=sum+n;
                }
                result -= result / i;

            }
        }
        if (n > 1) {
            result -= result / n;

        }
        return result;
    }


    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        } else {
            return gcd(b, a % b);
        }
    }

    public int sumOfFlooredPairs(int[] nums) {
        // long sum=0;
        long mod = (long) (1e9 + 7);
        Arrays.sort(nums);
        long[] numerator = new long[nums.length];
        long[] denominator = new long[nums.length];

        long[] numerator1 = new long[nums.length];
        long[] denominator1 = new long[nums.length];

        long num = 1;
        long den = nums[0];
        numerator[0] = 1;
        denominator[0] = den;
        long num1 = 1;
        long den1 = nums[nums.length - 1];
        numerator1[nums.length - 1] = 1;
        denominator1[nums.length - 1] = den1;


        for (int i = 1; i < nums.length; i++) {

            long gcd1 = gcd(denominator[i - 1], nums[i]);
            long lcm = (denominator[i - 1] * nums[i]) / gcd1;
            long n1 = lcm / denominator[i - 1] * numerator[i - 1] + lcm / nums[i];
            numerator[i] = n1;
            denominator[i] = lcm;

            long gcd2 = gcd(denominator1[nums.length - i], nums[nums.length - 1 - i]);
            long lcm1 = (denominator1[nums.length - i] * nums[nums.length - 1 - i]) / gcd2;
            long n2 = lcm1 / denominator1[nums.length - i] * numerator1[nums.length - i] + lcm1 / nums[nums.length - 1 - i];
            numerator1[nums.length - 1 - i] = n2;
            denominator1[nums.length - 1 - i] = lcm1;




           /* prefix[i]=sum;
            sum12+=1d/nums[nums.length-1-i];
            prefix2[nums.length-1-i]=sum12;*/

        }
        /*System.out.println(Arrays.toString(numerator));
         System.out.println(Arrays.toString(denominator));*/
        int sum2 = 0;
        for (int i = 0; i < nums.length; i++) {
            //float d1=(float)(numerator[i]/(double)denominator[i]);
            sum2 += (int) (Math.floor((numerator[i] * nums[i]) / (double) denominator[i]));
            sum2 %= mod;
            if (i + 1 < nums.length) {
                // float d2=(float)(numerator1[i+1]/(double)denominator1[i+1]);
                sum2 += (int) (Math.floor((numerator1[i + 1] * nums[i]) / (double) denominator1[i + 1]));
                sum2 %= mod;
            }
        }
        return sum2;


    }

    public static boolean[] primes(int n) {
        boolean[] p = new boolean[n + 1];
        p[0] = false;
        p[1] = false;
        for (int i = 2; i <= n; i++) {
            p[i] = true;
        }

        for (int i = 2; i * i <= n; i++) {
            if (p[i]) {
                for (int j = i * i; j <= n; j += i) {
                    p[j] = false;
                }
            }

        }
        return p;
    }

    public String LargestEven(String S) {
        //  char[] ar=S.toCharArray();
        int[] count = new int[10];
        for (int i = 0; i < S.length(); i++) {
            count[S.charAt(i) - '0']++;
        }
        int num = -1;
        for (int i = 0; i <= 8; i += 2) {
            if (count[i] > 0) {
                num = i;
                break;
            }
        }
        StringBuilder ans = new StringBuilder();
        for (int i = 9; i >= 0; i--) {
            if (i != num) {
                for (int j = 1; j <= count[i]; j++) {
                    ans.append(i);
                }
            } else {
                for (int j = 1; j <= count[num] - 1; j++) {
                    ans.append(num);
                }

            }
        }
        if (num != -1 && count[num] > 0) {
            ans.append(num);
        }
        return ans.toString();
    }

}