Problem: After you had helped George and Alex to move in the dorm, they went to help their friend Fedor play a new computer game «Call of Soldiers 3».

The game has (m + 1) players and n types of soldiers in total. Players «Call of Soldiers 3» are numbered form 1 to (m + 1). Types of soldiers are numbered from 0 to n - 1. Each player has an army. Army of the i-th player can be described by non-negative integer xi. Consider binary representation of xi: if the j-th bit of number xi equal to one, then the army of the i-th player has soldiers of the j-th type. 

Fedor is the (m + 1)-th player of the game. He assume that two players can become friends if their armies differ in at most k types of soldiers (in other words, binary representations of the corresponding numbers differ in at most k bits). Help Fedor and count how many players can become his friends.

Input

The first line contains three integers n, m, k (1 ≤ k ≤ n ≤ 20; 1 ≤ m ≤ 1000).

The i-th of the next (m + 1) lines contains a single integer xi (1 ≤ xi ≤ 2n - 1), that describes the i-th player's army. We remind you that Fedor is the (m + 1)-th player.

Output

Print a single integer — the number of Fedor's potential friends.

Examples

Input

7 3 1
8
5
111
17


Output

0


Input

3 3 3
1
2
3
4


Output

3

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class CodeForces
{
    public static void main (String[] args) throws java.lang.Exception
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int m=sc.nextInt();
        int k=sc.nextInt();
        int a[]=new int[m+1];
        for(int i=0;i<=m;i++)
        {
            a[i]=sc.nextInt();
        }
        //FEDOR
        
        int fedor=a[m];
        //System.out.println(fedor);
        Stack<Integer> s=new Stack<>();
        if((fedor%2==0 || fedor%2==1) && fedor!=1)
        {
               while((fedor%2==0 || fedor%2==1) && fedor!=1)
               {
                   s.push(fedor%2);
                   fedor=fedor/2;
                   if(fedor==1)
                   {
                       s.push(1);
                       break;
                    }
                }
        }
        else if(fedor==1)
            s.push(1);
        if(fedor>0 && fedor!=1)
        {
            s.push(0);
            s.push(1);
        }
        //System.out.print(fedor+" "+s);
        ///
        
        int friends=0;
        for(int i=0;i<m;i++)
        {
            Stack<Integer> s1=new Stack<>();
            if((a[i]%2==0 || a[i]%2==1) && a[i]!=1)
            {
                    while((a[i]%2==0 || a[i]%2==1) && a[i]!=1)
                    {
                        s1.push(a[i]%2);
                        a[i]=a[i]/2;
                        if(a[i]==1)
                        {
                            s1.push(1);
                            break;
                        }
                    }
            }
            else if(a[i]==1)
                s1.push(1);
            if(a[i]>0 && a[i]!=1)
            {
                s1.push(0);
                s1.push(1);
            }
            
            if(s1.size()==s.size())
            {
                int temp=k;
                for(int i1=0;i1<s1.size();i1++)
                {
                    if(s1.get(i1)!=s.get(i1))
                        temp--;
                    if(temp<0)
                        break;
                }
                if(temp>=0)
                    friends++;
            }
            else
            {
                if(s1.size()<s.size())
                {
                    int temp=k;
                    for(int i1=0;i1<s1.size();i1++)
                    {
                       if(s1.get(i1)!=s.get(i1))
                            temp--;
                        if(temp<0)
                            break; 
                    }
                    for(int i1=s.size()-1;i1>=s.size()-(s.size()-s1.size());i1--)
                    {
                        if(s.get(i1)==1)
                            temp--;
                        if(temp<0)
                            break;
                    }
                    if(temp>=0)
                        friends++;
                }
                else if(s1.size()>s.size())
                {
                    int temp=k;
                    for(int i1=0;i1<s.size();i1++)
                    {
                       if(s1.get(i1)!=s.get(i1))
                            temp--;
                        if(temp<0)
                            break; 
                    }
                    for(int i1=s1.size()-1;i1>=s1.size()-(s1.size()-s.size());i1--)
                    {
                        if(s1.get(i1)==1)
                            temp--;
                        if(temp<0)
                            break;
                    }
                    if(temp>=0)
                        friends++;
                }
            }
             //System.out.print(friends+"   "+s+"   "+s1);
        }
        System.out.print(friends);
    }
}