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 PYTHON3):

Solution:
from math import log


def convert_base2 (num,position_one=[]) :
    if num == 0 :
        return position_one
        
    else :
        ans = log(num,2)
        position_one.append(int(ans))
        num -= 2**int(ans)
        return convert_base2(num,position_one)


def find_friends(n,m,k,seq) :
    total_friends = 0
    seq.reverse()
    main = convert_base2(seq[0])
    seq.pop(0)
    for x in seq :
        diff = 0
        compare = convert_base2(x,[])
        for i in compare :
            if i not in main :
                diff += 1
                
        for j in main :
            if j not in compare :
                diff += 1
                
        if diff <= k :
        
            total_friends += 1
    
    
    return total_friends
    
    
n,m,k = list(map(int,input().split()))
seq = []
for x in range(m+1) :
    seq.append(int(input()))
    
print (find_friends(n,m,k,seq))