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:
def army(a,dict1):
    dict2 = {}
    binary =[]
    while(a != 0):
        binary.append(a%2)
        a = a//2
    for i in range(len(binary)):
        if(binary[i] == 1):
            dict2[i] = 1
    
    ans = 0        
    for i in dict2:
        if i in dict1:
            ans+=1
            

    diff = len(dict1)-ans + len(dict2)-ans
    return diff



n,m,k = input().split()
n = int(n)
m = int(m)
k = int(k)
lst1 = []
for i in range(m):
    lst1.append(int(input()))
a = int(input())
dict1 = {}
binary =[]
while(a != 0):
    binary.append(a%2)
    a = a//2
for i in range(len(binary)):
    if(binary[i] == 1):
        dict1[i] = 1
        
friend = 0
for i in range(m):
    diff = army(lst1[i],dict1)
    if(diff<=k):
        friend+=1
print(friend)